PLACEHOLDER
Carriers provide fighter support, which are basically suped up, very long range drones. They have their own control system so you should familiarize yourself with them, that is not covered in this guide (yet).
Light Fighters (LF): These fighters are used to attack other ships. They have a modest dps primary attack as well as a high alpha special missile volley attack with low rate of fire and limited ammo. They also have a microwarpdrive that lets them travel at extremely high speeds (12 km/s) for a limited duration. The four racial light fighters are slightly different and do their racial damage, it is not that important which race you go with.
Support Fighters: These fighters don't apply any damage but provide EWAR: neuting, ECM, webbing or pointing. Of these the webbing (Dromi) and pointing (Siren) fighters are the only ones that see any real use. The Dromi have a microwarpdrive like the LFs which the Siren has a slower afterburner. Since a recent patch support fighters can only be launched from regular carriers not supercarriers.
Space Superiority (SS): These fighters are used to attack other fighters. They have a primary attack, as well as a tackle ability which can shut down a fighters prop mod to prevent them running away. They also have an 'evasive maneuvers' ability which increases their speed a bit but also lowers their sig radius so they take less damage.
Supercarrier fighters: Supercarriers can also use heavy 'fighter bombers' (fibo). These are the heavy attack (called SR for short range) which are like the LF but for anticapital use and long range (LR) fighters for shooting subcapitals. LR fighters have a microjump drive instead of MWD and can also launch bombs which are a bit like stealth bomber bombs.
When carriers face off against each other an 'SS war' will usually ensue where they try to kill off the other side's fighters to gain fighter superiority.
When there are supercarriers on field, carriers can kill their fighter bombers with SS.
For information on how to control fighters read 'Controlling fighters'
Carriers also have something called an NSA which is basically a high-slot super sensor booster which increases your scan resolution. However it blocks you from warping, tethering or docking so it is important to only use it when you are supposed to. Getting this wrong can get you killed.
Links carriers are used together with dreadnoughts, dropping with them to provide armor/shield links.