Don't go off alone, try and stick with some cruisers to protect you from destroyers and later on to provide anti-aircraft cover. Don't stick at the back trying for hero sniper shots across the entire map. You need to strike a balance so that you push forward enough to draw enemy fire and support your lighter ships without charging off on your own and being focused down or hanging back so much you're no use at all.
Shoot AP at pretty much all cruisers and battleships. Shoot HE at carriers at least initially to set them on fire and put their flight deck out of action. It's preferable to shoot HE at destroyers but if you're ever needing to shoot a destroyer in a battleship things are going badly.
Whenever you're changing between HE and AP you need to take into account the time to change, you can preselect a shell type to switch to after your next shot by single tapping the key for it, but be warned if you fire one gun it will then set all of your guns reloading to switch to the new shell type.
Angle your armour, especially when going against another battleship you want to angle either toward or away from them so that you're not presenting your broadside at a flat angle to their guns. If you do that and they aren't reloading you're just asking to take a citadel hit (big damage).
Likewise, just because your guns are all loaded and a ship is in range doesn't mean you should take the shot. Ideally you want a target who is broadside on to you and to aim for the shells to hit around the waterline beneath the turrets or funnels. So if you see a target who is turning, waiting a few seconds and hitting him whilst he's side on is greatly preferable to shooting as soon as your guns are loaded and having half your salvo bounce.
If you get set on fire don't hit repair (R) immediately. A single fire will cause light damage over time and once it is near it's end you will be able to repair a large amount of it by using your T ability. If you get 2 or more fires going then use the repair ability.
The T ability will not repair citadel hits or heavy damage.
Keep an eye out for aircraft, I generally try and turn toward an incoming torpedo squadron and focus them with my AA (Ctrl click them), sometimes turning away can be the right thing depending on the situation but basically to dodge their torpedoes you need to be evading before they drop them, don't wait until you see them in the water to start turning.
Use the minimap, especially try and know where enemy destroyers are in relation to you. This will allow you to know how risky it could be to take a close course to an island for example.
For your first three captain skills I would take Basics of Survivability, Expert Marksman and Superintendent.
Lastly, people come to this game with ideas about what battleships should be and moan when the reality in game doesn't match up. You're a big slow target. You have a lot of armour and a lot of health but if you don't play smart that can all be wiped out by one sneaky destroyer. Your guns can be utterly devastating but are also very inaccurate, so you need to pick your shots, angle your armour and use your abilities well to maximise your staying power.
Hope some of that rambling is useful, have fun
