First off, it must be understood that in Counter-Strike: Source (CS), there are several different map types. These types are:
Bomb Map (de)
The Terrorist goal in a bomb map is to run to a specific location (marked on your map) and plant an explosive. The explosive is on a timer, so once it is planted, you must defend it until detonation.
The counter-terrorist goal on bomb maps is to prevent the terrorists from planting the bomb at all costs. This can be done by eliminating all of the terrorists, defusing the planted bomb, or (in some cases) defending the bomb site until time runs out.
Hostage Rescue (cs)
In hostage rescue maps, the primary goal for counter-terrorists is to rescue hostages captured and held by the Terrorists. You can also win by eliminating the terrorist team.
The Terrorist goal is to simply prevent the counter-terrorists from rescuing the hostages by eliminating them, or maintaining control of the hostages until time runs out.
Bomb Maps - Counter-Terrorist
As a counter-terrorist on bomb maps, your best bet (by far) is to eliminate the terrorist team before they can plant the bomb. Defusing the bomb makes you a sitting duck, and this is a situation you want to avoid. Keeping the terrorists looking to plant the bomb means you get to stay on the defensive, which gives you an advantage.
Bomb Maps - Terrorist
As a terrorist, your only goal is to completely overrun a bomb site. If you can not take control of a bomb site within the first 30 seconds, your team will likely lose the round. The best strategy is to rush everyone on a team except for 2 or 3 (tops) to a single site. The other few players will act as a distraction at the other site, so the counter-terrorists guarding it do not come in as re-enforcements.
Hostage Maps - Counter-Terrorist
I have found the best strategy to be spreading the team out and attacking from all angles. Coordinate a simultaneous attack if possible, but be sure nobody just "runs in, guns blazing," because that technique almost guarantees death in a hostage map.
If one side of the attack manages to punch through and get inside the area under Terrorist control, the rest of the team should move to that area in order to assist the attack.
Hostage Maps - Counter-Terrorist
As terrorist, your only strategy here should be to sit and wait. Your goal is for them to come to you. Sit, Wait, and SHOOT!
Shoot a round out of your pistol at the beginning of the match. When you think (or hear) an enemy nearby, switch to your pistol, press reload, and quickly switch back to your main rifle. Most enemies will jump out and attack when they hear the reload sound, because they think you are defenseless.
This has become a staple of counter-strike over the past years, but some players do not quite understand it. If you are in a firefight at range, you can strafe-shoot to maintain accuracy but still make yourself a difficult target.
The way strafe-shooting is done is by pressing (or tapping) the strafe key to get your player moving and releasing it just as you begin to fire. Your player will continue to move for another step, but your shots will be accurate.
The AWP No-Scope
Many people have had problems with this, and it is really so simple. A No-Scope shot is when you shoot an opponent with a sniper rifle without using the scope. For all sniper rifles, the cross-hairs have been removed when you are not using the scope, and the weapons are incredibly inaccurate. This was done intentionally to force people to use the scopes on sniper rifles. The problem with the scope is that it is difficult to make short-range shots, and your player moves very slowly while looking through it, so you become an easy target. The solution to this is the No-Scope shot.
The No-Scope is done simply by pressing the right and left mouse buttons at the same time while your intended target is as close to the center of your aiming point as possible (you have to estimate this). The scope will pop up for a small fraction of a second, and your shot will be accurate.
You will notice after playing Counter-Strike for a long time that most players follow very predictable patterns. Ammunition is expendable, and any of the rifles (AK-47, M4, etc.) will penetrate through about the first 3 inches of a corner. When approaching corners that likely have opponents on the other side, shoot the corner. You will often hit your enemies before they see you.