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Counter-Strike is all about playing as a team. If you don't work as a team, you will loose. It's fairly simple concept. Playing as a team may mean you can't just do as you want, but what is best for the team as a whole.
You should look at your skills and make sure it isn't being used in the wrong place. Work with the team, use your radio to synchronise your attacks. Discuss in dead talk what you plan to do next round.
Keep alert about your situation. If you are working in a close group, make sure that there is somebody watching the rear at all times, if nobody else is, then you do it. If you are working in a pair, get used to check your side of the corridor and letting them check theirs. Take it in turn to open and enter through doors. One of you can open the door and the other person dives through, take it in turns to keep the risk fair.
Knowledge of the level helps, because if your team gets stuck in a rut, you can then go and take the flank, assisting your team in getting through. Team play definitely takes the most amount of thought in the game. Doing the right things to come of most effective. If you pair up with somebody who is sneaking around without making a noise, running about behind him is not going to be effective team work - in-fact that will destroy it even more.
A good team has a variety of skills. Long range snipers, medium range assault and close combat players. Find the empty patch on the team, and fill it, and provide the correct fire power for it. There is no point having a sniper rifle and rushing, leave that to the close range players. If you find that your team is winning and everybody is buying sniper rifles - bin yours (it's not real money, it doesn't matter), and buy an assault rifle.
The best trick I know with team play is being able to understand movements. In real life we use body language to instruct people. We can point, and make gestures, this can't be done in Half-Life. The nearest form is being able to move your character in a certain way. If you have somebody who looks at you then a door, you then a door, and so on - chances are he means go first. People who stand still jumping next to an object often want a boost onto something else. Give them the help they want. Flashing a light once usually means "Hello, I'm a good guy, don't shoot me". More than that often means "follow me". The ability to communicate without speaking in the game gives you a massive advantage over the enemy. You are most vulnerable when you are chatting, as your controls are effectively dead.