Here, kills are not as important as team victories, and few players go with no deaths. The only way to win is to work together. General Tactics Counter Strike is a team game, more so than nearly all other first person shooters. Working as a group is extremely important, especially in large games, where running into groups of four or five opponents is fairly common. Always try to find a couple of guys who seem to do well and run with them.
Most people appreciate the backup.
Always give the person a little bit of space when you are behind them. There is nothing worse than taking fire and trying to backup, only to find that someone is directly behind you, preventing from moving and more often then not getting you killed. Most of the time, a couple lucky bullets will take out whomever you're trying to kill, many times without taking any damage at all. Above all else, try to change up what you do. If you hide behind some boxes on one round, you can bet that the next few rounds your opponents will check that spot.