Well there are a lot of elements that matter in this game, not limited to the following:
1) Aim
2) Weapon knowledge
3) Team coordination
4) Recoil control (this applies separately to all weapons)
5) Movement control (knowing how to stop quickly and take a quick, accurate burst is very important)
6) Map knowledge
7) Sound awareness (listen for your enemies)
8) Game sense (sensing where your enemies might be...playing a lot will develop your game sense)
The more you play the more these will improve.
Here are some tips:
To improve your aim, it's important that you have your mouse and sensitivity configured correctly. Make sure you don't have mouse acceleration on (in your Windows mouse settings, uncheck "Enhance pointer precision". Next, I suggest you don't keep sensitivity too high. The lower your sensitivity, the more consistent and precise you can be, at the expense of a slower turning speed. My personal preference is to have it so that a full swipe across my mousepad (11") rotates me 270 degrees in game. You might want to have it higher than that if you're not accustomed to a high sensitivity but I wouldn't really go more than double that if you can.
Weapon knowledge...all I mean here is knowing what weapon is good and in what situation. For most cases, I'd recommend you stick to buying the following weapons: P250, MP7, P90, AK47, M4A1/M4A4, AWP. There may be situations where you'd want a Nova, Mag7, AUG, or auto-sniper, but the former should have you covered. A reduced arsenal will make it easier to get practice with the most used weapons in the game.
Team coordination and competitive game flow. It's important to know when to buy, what to buy, and how to play as a team. If you win the pistol round, I recommend that most of the team goes with MP7s for a few reasons: you get more money per kill, your opponents are unlikely to be wearing helmets so the MP7 will be particularly deadly, and if you do lose you'll only be giving your opponents SMGs, while you'll still be able to afford weapons the next round. After that, coordinating money is important. If only some team members buy and others do not, you're likely to lose the round. If everyone can't afford a rifle, vest, and helmet, it's usually a good idea to save for a round. For a save round, the P250 is a good weapon, as is the Nova in certain positions.
You can practice recoil control by yourself in game. First off, know that for most guns, you don't want to be moving while shooting them (though SMGs and shotguns can be an exception to that). You'll have the option of either bursting, or going full auto. If you're bursting, it's good to side step in between bursts. Every gun has a different bursting ability. The AK47 is accurate on it's first shot, and nearly just as accurate on it's second shot, so one or two shot bursts are recommended. For the M4, especially in the case of the silenced one, it can be accurate on its first two shots, and the third shot might just go a little high, so you can do two or three shot bursts while bringing your mouse down for the third shot. The best thing to do is to just practice against a wall in a local game. Practice side stepping and bursting a target. For full auto, you want to probably be at a standstill. Every gun has a somewhat predictable spray pattern. Go in a local game, spray at a wall, and notice the repeated pattern. Learn to counter that pattern and try to keep your bullets going in the same place...this takes a lot of practice.
Movement control, map knowledge, and game awareness should come with time.
For sound awareness, you'll want to be playing with headphones will having the volume high enough to hear footsteps, reloads, weapon switches, bomb plants, and other sounds which will help you pinpoint enemy locations.
