Understand your game. Learn everything about the maps you play on, such as vantage points, secret (or just less visable) locations, areas where players are the most vulnerable. Learn the weapons , how to use them in more than one situation effectively.
Develop good instincts. Learn to shoot when something moves. Throw a grenade if you can't see your enemy.
Read about game, and further your knowledge of it. Learn about strategies, tactics, and use this to your advantage.
Practice, practice, practice!, with your guns and grenades. For example, find safe points in room and memorize how to throw the grenades into popular camping points.
Concentrate on when you see your enemy, and when he sees you.
Read your enemies. If somebody spots you, you're now engaged in what I call a "mind war". For example, if you plant the bomb , the enemy will know your general location. You can either guard the bomb, strike while they're defusing, or run the map looking for the enemy. On the other hand, if you're playing the opposite team, think about where your opponent might be waiting or watching.
Play against good players. You won't get anywhere killing newbies all day.Learn it the hard way from the top wolves themselves.
When you find a player who isn't a jerk and you get whooped, talk. Make friends, ask questions, get answers, and learn. Give them the occasional "Wow, where were you?" or "How did you do that so fast?". They're bound to share some tips with you.
Play often. If you skip out for a few days, you're going to get rusty. Also, play in medium bursts, around two to three hours per session, two to three times a day.
Never give up! Giving up usually means you've hit your peak, though you have more to put out. Some players quit and hate the game because of a bad match or two, or an embarassing moment. Unless you have a problem with the game itself, and it's not some anger issue, quitting should never be an option. Just remember, "Progress over time, and victory is mine."
Play with friends. It makes the experience more fun, and you can have those post-games talks about what went right, wrong, and how to improve. Plus, you have people to cheer you on when you win, and pat your back when you don't.
Never, and I mean never, play music while you play the game. It takes a piece of your mind that could be used for concentrating, and it wanders off and pays attention to the music. Unless you're a "vibe" player (using music to keep your emotions calm, while normally they're hard to control), music is not recommended.