I use to own at counterstrike till I left school (not to brag but several times I took out entire teams after my whole team had died and I was starting with no armor and a handgun). Now I have a crappy 56k connection and I tried it a few times but it always disconnects me, so no CS for me. But you don't care about that, so here's some stategies that work for me:
1) In the beginning of the round its ok to run to whichever position you want to take, but after that you should walk EVERYWHERE cause they can hear your footsteps. Only exceptions should be when you want to rush in on hiding enemies or if you need to run across a corridor to avoid being an easy target.
2) Always crouch when you shoot. Learn to immediately hit the crouch button as soon as you see an enemy. Crouching greatly increases accuracy.
3) Always aim for the head. You'll end up having a better aim, and you'll be hitting them in the head!
4) Learn the AK-47 and the CT's silenced gun (can't remember its name, but use it without the silencer) - they are the 2 most powerful.
5) When you die, watch enemy tactics. Eventually you will learn trends that most sh*tty players do on maps all the time, like hiding places, routes, etc. And you'll know how to be ready and counter them.
6) Learn & remember the maps.
7) If there's noone on your team left or very few people, I see no problem getting a nice sniping position till you even out the odds (although most people will bitch and call it camping.)
8) Travel in groups, and rush key positions. If your teammates want to all do their own thing, yell at them until they cooperate. If they don't cooperate, leave the server and find one that isn't full of retards.
9) Listen for footsteps - wear headphones because it's much more distinct that way, you can tell where people are and ambush them... also pay attention to your radar so you know if its your teamates.
10) Be ready to switch to your handgun if you're in at close range - when both people run out of ammo on their primary weapon, you'll have the advantage while the other idiot's reloading.
That's all I can think of right now, but 10 is a nice, round number.