Please note that this is not an attempt to turn Battlestar Galactica into a hard science show, nor even attempt to explain things using modern knowledge. Instead it is intended to give some answers in vague terms on how things work for purely a background or role-playing note. A lot of information is taken from the original novels.
Whilst most of this information is written from a Colonial point of view, it applies equally to the Cylons unless stated.
For notes on these notes, see here.
There are types of movement systems needed in space - sublight and hyperspeed.
Sublight travel is how a ship moves anywhere within a single star system. Generally the speed is below the speed of light (hence the name) and travel times within a system will take a few centars or less. All combat between space fleets is conducted at sublight speeds.
Hyperspeed travel is sometimes referred to as Hyperspace travel or light speed. The act of entering hyperspeed is sometimes called jumping.
Hyperspeed travel is needed when a ship needs to move to another star system. When the ship enters hyperspeed, it appears to disappear from view. When a ship exits from hyperspeed, it it 'blinks' into existance. In actual fact, the ship is just travelling faster than be detected. Travel through hyperspeed takes longer then sublight travel, from a few centars to days for long jumps. Once in hyperspeed, the ship is effectively cut off from the rest of the universe except for some forms of communication. The ship does not actually leave the known universe though, and while man made objects will not be able to intercept the craft, it is still effected by objects like planets and stars, and man made minefields will still hinder a ships travel.
An excellent example of hyperspeed travel can be seen in the Playstation and X-Box Battlestar Galactica game. This shows the travel perfectly.
Colonial ships move via their Marron hyperdrive engines. These engines propel a ship through hyperspeed towards their target destination. The drives are named after the woman who invented them. It works by creating a hyperspeed field around the ship and then speeding the ship to the new co-ordinates. The time taken to travel to a new system depends on the power of the drive and the distance travelled, and can take a few centars.
When exploring into the unknown, the time to program a jump to hyperspeed rises enormously as the exit point has to calculated from unknown variables, and this can lead to errors, resulting in either a different exit point or a mis-jump, and potentially loss of ship. As a result, these kind of jumps are not rushed. A ship without long range sensors able to locate stars, planets and other spatial features is not going to be able to make any trip through hyspeed.
The Marron drive does not work well in a stars gravity well, which means that ships jumping into a system actually enter at the systems edge and then have to travel inwards at normal sublight speeds.
Also the field that forms around the ship at point of entering hyperspeed (to protect the ship from being destroyed when travelling so fast) is effectively 'skin tight'. This means that a carrier ship has to recall all it is satellite vessels before entering hyperspeed, and thus the most vulnerable time for such as carrier is the moment just before and after hyperspeed as the ship will not have any fighters in the air.
Through normal space, ships move using their ion drives which work by burning fuel and expelling the exhaust which propells the ship. Whilst very efficent, capital ships have a problem in that they cannot travel very fast using their ion engines without some considerable effect.
As an aside, ion engines do leave a trail which makes them easy to follow with the right sensors for a short time.
The Cylons use a different form of motive power than the Colonials, using a gravitic drive for movement. This seems to make their ships slower than comparable Colonial ships, but the drive itself is buried deep inside the ship and thus far less susceptible to damage.
It also allows the ship differing movement capabilities (such as the fact that Baseships can rotate while moving) and seems to be used for both hyperspeed and normal sublight travel, although when moving as a hyperspeed vessel it seems to suffer the same limitations as the Colonial Marron drive.
The range of hyperspeed for a ship depends on its long range sensors. The further a ship can see, the further it can travel. For civilian ships, this limits them to travelling to the next star system. For military vessels, the range is about equal to two star systems travel. Theoretically, a ship can travel through hyperspace for as long as it has fuel. However, as a craft is generally trying to outrace its sensors, this is not practical.
This is variable based on the range that is going to be travelled. A typical short range trip will only take a few centons (such as from Cimtar to Cyranus), longer journeys will take much longer (such as from the staging point after the ambush to Carillon).
Colonial craft use Tylium as a source of fuel. In it is natural form, Tylium is a solid mineable substance that is fairly stable, although explosions and fire near it can set it off with dramatic effects. This form is then refined into liquid Tylium which is actually used as fuel for the Colonial Fleet. In this form, it is very volatile and if handled incorrectly will likely explode causing more damage to the carrier than would be liked. However, this volatile nature is what is prized about the fuel, and the amount of energy it can give out when burnt controllably in an engine is out of proportion to the amount carried.
Vipers can travel at hyperspeed, although their speed and range is more limited. Fighters are generally restricted to two trips at hyperspeed. One to get to a system and one to get back. Further trips require refuelling.
At least the range of 1 star system. At this range the ship can detect planets, suns and other major planetary anomolies. Also it may detect enemy ships - large ships (Baseships) may be detected as baseships, smaller craft (Raiders) are detected as small craft.
Short range sensors are able to scan a solar system from anywhere within that system. They can pick up all planetary objects, vessels (and type) and other anomolies within the system. From outside of a planetary orbit, they can detect lifesigns and main cities on planets. From a planets orbit, they can pinpoint cities and make fairly detailed scans of structures, although they can not actually determine amount of life signs or determine interiors of buildings. Sensors are blocked by planetary objects, so ships can hide behind planetary bodies and not be initially spotted.
Vipers sensors are much like a Battlestars short range sensors, although not quite as accurate or precise. Vessels can be identified automatically, but the type of vessel is not known until the ident has been run through the Vipers Warbook. Vipers can feed their sensor feed back into their command ship thus increasing its range, and vice-versa - although this will not increase the vipers range, it will mean that the Viper does not have to rely on its own sensors.
Communication technology is limited to within short range sensor scan range only. However communication is almost instantaneous within this. Most short range communication signals are broadband, thus able to get to the maximum amount of targets in the minimum amount of time, although this has the disadvantage in that anyone within range has the ability to intercept these messages.
Military and more secure ships use tightbeam messages for added security. These messages are targetted only at the recipiant ship thus making interception a lot more difficult as the enemy has to be within the two ships. Most of the time tightbeam communication is done via line of sight, so planetary bodies will block these messages naturally.
Short range communication signals can include voice, video and data elements.
Signals can be sent at longer ranges, but this takes a little bit of time to send and is limited to codes only, not voice or video. These signals are also tightbeam meaning that they have a specific direction and thus if intercepted their origination and destinations can be determined. Thus they are not often used by military ships. Signals can be picked up by all sides, and most ships have decoding equipment - it is not uncommon for rouses to be made by one side sending messages knowing the other side will pick up those signals and act on them. Civilians use these signals, especially for televised broadcasts for important events, and then they include sound and vision.
Signals can be sent excrypted and encoded for additional security (these codes change frequently enough so that interception is not usually a problem), and can be classified as priority for urgent messages.
Turbolasers are not actually true lasers, but rather a more directed form of energy weapon. For a start, the weapon can be used a 'proximity' weapon, so the charge will explode at a certain distance meaning direct hits are not always required. This charge allows impact damage as well as energy damage. Because this is not just strictly energy, the weapons do actually have an amount of charges and can not be used indefinitely. When a fighter docks at the mother ship, it does have to reload and re-fuel. The term laser-torpedo is a more acurate term and it sort implies a physical and energy part.
Cylon ships also use turbo lasers and pulsar weapons on their ships, but the way they function is different. While it is not known how they work precisely, it is known that they give off large amounts of di-ethene gas, which can be fatal to human life. this was also a way of detecting early Cylon Asteroid ships - after a combat encounter the asteroid would be covered with di-ethene gas which could be detected by Colonial ship - if they had a suspicion that a Cylon could be lurking nearby.
Secondary weapons carried by some ships include the missile launcher. Missiles have their place in space combat because the warhead that can be carried by the ship can be devastating if it hits. Unfortunately getting it to hit can be a problem as there are many ways that the missile can be intercepted because it reaches it is target, or it can be jammed or shot down by the target ship, and as such they are usually close range weapons or used in planetary bombardment. Colonial doctrine is to use missiles offensively - their ships get close to the opponent and then they fire a full barrage. Coupled with fighter cover, this is usually enough to overwhelm a ships close in defences and inflict major damage.
Cylon missiles are usually slow drones that are more intended for planetary bombardment than actual space combat, although they can have their uses, especially when used to swamp a targets defensive systems.
All military vessels employ electronic defensive screens of some sort. They fill the space around the target ship with electronic static and countermeasures in an attempt to fool target and tracking computers. They can also interfere with missile guidance systems. As such, they make it harder for an enemy ship to hit the target, but if the target is hit, then the damage it receives is completely unneffected. The closer one gets to the enemy ship though, the easier it is to actually penetrate these shields and thus void that crafts ability to protect itself.
Fighters do not tend to carry shields of these sorts because they only carry enough power for their speed and weapons. Their small size tends to protect them against a capital ships weapons. A capital ship too, tends to not have much defence against a fighters attacks as the fighter generally gets so close to it is intended target that if the computer can not lock on, the pilot has a better than fair chance of hitting the target ship using just his own vision and instincts.
The main defence of a ship is it is armour. Every ship, be it Colonial or Cylon is usually covered in a thick layer of protective armour. While this armour does protect a ship in the conventional manner, it also protects a ship against energy weapons by spreading that energy across a much wider section of the armour than was hit, and this allows it to bleed that energy back into space.
Force field technology does exist, but not in a combat role. Instead force fields are used for blocking and barring openings to the elements and personal. For example, Colonial Warrior helms use force fields to shield the pilot from the vacuum of space. Whilst they can not be used as space suits, the helms can be used as breathing units, the field keeping the air in. Landing bays use force fields to fill the space that craft land in. Again, the landing bay looks open, but a force field stops the air leaving the bay. Finally, another important role for force fields is in prisons. Prison doors integrate force fields to keep their occupants in place.
Colonial medical technology is quite advanced. It has decontamination units that quickly and efficently destroy alien viruses and germs. It has bone setters that can repair and fuse broken bones within minutes (and make them stronger than before), cyro tubes that can lower the temperature of the body to allow it to use less resources (oxygen and the like) making is survive for longer until cures can be found. DNA mapping and matching can be done to determine biological parents, and a wide range of anti-viral cures are available, most simply requiring a pill or hypo spray injection. Results are usually quite quick to see. Obviously because the war has been going on for so long, medical advances were bound to happen.
Cylons to have a wide interest and knowledge in human anatomy, and their abilities in human medicene is also good. Unfortunately this is mainly because they use it to torture and keep alive their prisoners.
The Colonials have developed methods of rapid plant growth, able to grow plants in a day, and have them ready for harvesting in two or three at most. The technology exists to allow for plant growth in almost all conditions providing some natural light and heat exists (and thus these techniques do not work on ice planets). This process is used a lot to help feed the Colonial people, especially the world Aeriana.
The Colonials have great simulator technology. It can be compared to Star Trek Holodeck technology, but is slightly different. Everything produced is illusion with only limited tactile response and the range of area available is limited to the size of the simulator. This means that nearly any sort of terrain can be produced and scampered over, but set piece ground battles must be limited in their size. Viper pilots have it slightly differently. There is no limitations to the amount of space that can be produced but to get this,each Warrior must be seated in their own cockpit simulator, although these can be linked together. Simulators are used to train Warriors and are mainly used in ground academies where they can be built to large sizes. It is rare for ships to have anything but a few cockpit simulators, and then only large vessels will have them.
Colonial simulators can reproduce Cylon opponents quite accurately, but have problems trying to detail humans, both in response and appearance.
The Colonials also have another form of simulator technology, developed by the Sagitarians, called Fantasy Interplay Technology. What this does is project fantasies directly into the users mind. It plays to the senses in via the mind, and thus to anyone standing next to the user, they will see nothing. However, the same images can be projected via a screen, although this will lose a lot as to the user, they are actually in the situation. It is hardly used for military training, however it is used a lot in the entertainment industry, especially the gaming community. It also has its medical uses as well.
Cylons however, do not tend to use simulators much, if at all, for training. Instead, they use small portable devices that are used solely to project the image of a single person, usually someone that the Cylon wishes to study for tactical purposes. This device is programmed with as much information as the Cylons can find out about them - mainly from prisoners - and thus the device is only as good as the programmers. However, with the right amount of information, the device can be very accurate in its protrayal.