My tips from years ago of playing CS..
Use these weapons in order of cost: usp/deagle/mp5/ak/m4/awp. Honestly, dont bother with any other weapons. There
is a reason all the best players use these. The AK is the best gun in the game once you've mastered it.
One that no one else has said yet;
buy armour. Vest alone wont protect you much from your average public player aiming at the head (but will against grenades) but its still well worth it. Buying armour and a deagle will undoubtably get your further in a round than buying an M4 and no armour. Check your armour level when buying. If it's over 50% you dont really need to buy it again. Unless you need to add the helmet.
As for sensitivity --
lower it. This isnt Quake.. 9 times out of 10 your enemy will be far enough away to let you make time to aim. A low sensitivity will make it so much easier. There's no point talking numbers at you, as everyone's setups are different -- so do this: Set your sensitivity so that one 'swipe' across your mousemate turns you 90 degrees (*acceleration should be
off). Adjust it mildly until you're comfortable. Bear in mind it might take you at least a week or so of regular playing to get used to using you
whole arm to walk around. This is the idea. Dont worry if you fail miserably for the first few days -- it'll happen. Most players cant get used to using the whole arm, rather than just the wrist. Use your arm to move around and your wrist to adjust your aim once it's close to a player. Get used to 'swiping' across your mat. If its one swipe to 90 degrees, it's two to turn 180. It's not as slow as it sounds.. the aiming is far more beneficial than the minute chance you'll be able to kill someone that comes up behind you (although its still very possible, especially with CSS).
Two shot bursts are your friends, not 3. On most guns (iirc) only the first bullet is accurate. Aim for the neck and the second one will headshot them; the third would just miss. The AK is the king of two-shot bursts -- iirc it's first bullet is 100% accurate.
If you're close --
spray. Learn to control it. Start aiming at the chest then pull down to the feet. Even further with the AK. The M4 is the king of spray. I'm trying to think of distances, but say in Aztec if you're a CT at the top of the stairs (out of the water) and the T's rush the doors, it would be a 50/50 decision whether to spray or not. Any closer than that and spraying is your best bet --
especially in Source. That might seem like a long way off but it's do-able with practice. The M4's spray is more controllable when using it wihtout a silencer. Use it with the silencer for long distance bursts; this might just be psychological though
What goes without saying; dont move when shooting. Get used to stopping yourself with a quick tap in the opposite direction you're running, then firing almost simultaneously. The faster the better. If you're using the MP5 you can run around like a loony, it doesnt make any difference.
Um, have fun.. ignore 99% of what people say in chat
EDIT: (Wow i cant believe i just wrote all that for a game i gave up ~4 years ago!)