Pretty much what faceless said. Just play the game, enjoy, have fun, you will get better in the meantime. Bad Company 2 was the first FPS I played seriously online, I began very weak but eventually I got better.
When I started playing BF3 I had a really hard time adapting to the lag/controls but I think I'm kinda good now! Nothing exceptional but I hold my own.
First thing to do is add some gaffers. Don't expect people to add you, go after then, ask their PSN ID's and join their games. I would recommend Olimpia, thn, Boatack, faceless but frankly there's dozens of skilled players here, those are just the ones that are online more often. PS3 gaf is AWESOME! Some of then are really active in the forum. If you want look at my profile for my PSN ID!
Get to know the maps, you will learn then by playing the game,
but here's a site with some pictures.
Don't worry about not having a headset, coordinating is good, but most gaffers don't speak that much while playing. And then there's the ones like me who talk a lot but no one understands since my english is rubbish!
Stick with one gun until you unlock some sights (red dot, holo, etc) then if you want you can try another.
Only engage armor if you're playing with an engineer or a support with C4, if not let other people deal with then. Every class is useful in every map, but try to be mindful of their characteristics. In the end play with whatever class fits your style/tastes.
Please don't forget to drop ammo packs if you're a support (free points!), health packs and revives if you're an assault (more free points!), if you're an engineer fix your teams vehicles (even more free points!), if you're a sniper plant spawn beacons in strategic positions and movement detectors (not that many points, but still important and mostly free! Lol!).
And please, I can't stress this enough, if you're in a vehicle (tanks/ attack choppers mostly) only bail when you're pretty sure they will be destroyed! Letting an enemy steal your armor can mean the end of a game, specially a close one since your team won't spawn a new vehicle until the stolen one is destroyed!
Don't worry about stats, they're mostly useless, specially in a game like BF were K/D don't mean much.
Welcome aboard!!!