Use your radar. All the best players spend most of the game watching their radar, with it you can quickly form a strategy, see where your opponents are and where to expect them. Players who are oblivious to their radar will often find themselves running into ambushes or being chased down from behind.
Try to keep moving, new players often forget this and just stand still whilst trying to aim at people, it makes them a sitting duck to headshots from powerful weapons.
Keep these things in mind and you should do alright.
QFT.
If you have a Phantom and it's about the best weapon in the loadout, you might stay still and shoot, but most of the times you're better of moving and dodging bullets. While your accuracy decreases, your chances of survival increase as well.
About the radar: it's mostly about knowing the map and simple mathematics. So basically while you're moving you're looking for a position where you can be seen by as few players as possible, which maximizes your chances of survival.
E.g.: there's a T-shaped hall (-> like in Caverns) and your standing at the bottom of the T, while you know there's a firefight going on from left and right. Just don't move out in the open, or you'll be fired at by both players. Wait until one is dead or comes to you - then he'll be the one sandwiched between two players.
I do use the cross hair to aim. I'm not really good at aiming without one.
Try to use your crosshair less often - it's good for long distance shots or shots with the golden gun, if you really need it because you can only hit a pixel or something. Instead try using the bullet tracers as a guideline (pick up an RCP 90 and you'll know what I mean). Play some rounds of LTK and you'll be improving, at first hitting "at least something" until you're good enough to give headshots with the golden gun while running around.
