Never stay in one spot too long, or fire too many rounds in short succession. These are the things that will give you away quickly. A good method to use is to fire 2-3 shots, then duck for cover, spin and scan the immediate area, then go back up and scan the target area for snipers first, then other targets next. You will want to do a quick scan without a scope or binoculars first, and look for potential spots to investigate further. Once you do a quick scan, then look over the same area with a scope, and check for threats. Once you feel there are no threats, time to look for targets. It does no good to look for targets first, as another sniper may be looking for you. You will want to do this whenver you reach a new spot, or after you have been in a spot for a while. Remember though, the longer you stay in one spot, the greater the chance someone will get you.
Stay alert, and remember, in a FPS game, people will stop looking for you in a minute or two if you stop shooting. You can duck and cover in one spot, fire and duck again for a whole game, if you only fire a few shots, and stay hidden for a longer time. You can still get a good score, because you are on station for a longer amount of time.