If you look around the internet you can easily find the equation of how experience is rewarded. But lets not be that intricate. Basically you get a base XP, which you see at the end of the match on the ranking tab, and then based on what you do in game bonus XP is awarded, then additional bonuses, flags, camo, first battle modifier is added as well. In addition credits is figured out in the same way. Commander XP is based on your base xp awarded, then other bonuses are added although the modifiers are not as much. Free XP is figured in the same way as Commander XP.
First off, and this is important, its not how many KILLS you have but HOW MUCH DAMAGE YOU DO!! Damage is more important that kills. The more your damage the higher your XP.
Artillery hits (overpens etc), including secondaries, are not worth a lot but the more the better. Torpedo hits are worth a lot more.
Citadels are worth a lot of XP.
Fire and Flooding DAMAGE is also worth a lot of XP.
Causing a Fire or a Flood without damage isn't worth a lot of XP but if you happen to cause a lot of them it does add up. I once caused 10 fires in one game, less than 500 damage, but received a lot of XP.
Capping a control point gives you a lot of XP, capping alone is obviously worth more than if someone is in the control point with you. Capping in a normal battlemode, only 2 capture points, is worth more than the multiple capture mode.
Defended flags are a goldmine. If your out of the cap zone and there is a bot inside any time you hit will not only restart the capture timer but you will be awarded a Defended Flag, its not 100% guaranteed, I don't know how its determined. But a lot of Defended flags = a lot of XP.
Its hard to track what an Incapacitation actually is, not sure whether it is a damaged or destroyed module, turret, AA, torpedo mount, or steering. I don't really put my hopes on getting a lot of incapacitations.
Shooting down planes does not give great rewards.
Remember when I said the damage is more important than kills? That's not entirely true.
A Tier VII Battleship will receive decent XP for getting a KILL on another Tier VII ship. However, getting a KILL on a tier VIII or IX will give greater rewards. Conversely by killing a tier VI or V ship your reward will be much lower.
Basically the more you do, more flags you get in battle, the more XP you awarded.