As Uchiha said, shrink your crosshairs. It doesn't affect sniping whatsoever, but it improves your aiming many times over.
In console, type: cl_crosshairscale 2000
This makes your crosshairs rather small, but here is the bonus: You get that crosshair on somebody, you WILL hit them if you are standing still. It increases accuracy, as there is so little crosshair that if those lines touch them, you will most likely hit them. Personally, I run on a 2250 crosshairscale, but that's me. Whatever your preference.

Anyway, back to sniping.

Scout is better. The AWP costs a ridiculous amount, you will hit NOTHING if you move at all while trying to shoot, everyone hates you for it, and it is banned. Of course, I like to use the awp when I can, but you don't get that great satisfaction for killing someone as you do with the scout.
The scout gives you an amazing speed to run around (the AWP makes you slow as hell). It also reloads quickly, shoots faster, and is all-around a faster gun.

Now for tips.
1) Carefully set your mouse sensativity. Keep it at something that's comfortable and you can aim with, yet high enough so you can look around quickly. Personally, I often scan the areas about me often.
2) Know your terrain. Know where enemies come from, the typical spots they will be, and also ideal spots you can snipe from. You do not usually see a sniper standing in the middle of nowhere, wide open, and live long at all.
3) Don't double-zoom, unless your target is really far away (i.e. cs_harvest). It decreases the amount of surrounding area you can see, which is vital in spotting other other potential dangers.
4) Communicate with your team. While a lone sniper is helpful and may take out any threats, they are more of a "scouter" ( ;-) ), and are invaluable in locating targets.
5) Don't move and shoot like an idiot, unless you're in point-blank range. It's pointless.
6) When zoomed in with my sniper, instead of clicking zoom enough times to revert back to normal vision, I prefer a fast-switch to my knife/sidearm. The sidearm is typically ideal if you need stealth, cause the knife makes that indicative noise. The knife, though, is good for fast movement (and I love to hear that knife-draw sound).
7) Turn on fast-switch for weapons. That way you can accomplish the above easier, and don't have to deal with the typical hastle of changing weapons.
8) Strafe and shoot is invaluable to the sniper. You must be quick to aim with this, but here is the quicky on how it works.
Step to where you can see where you suspect your enemies to be, but strafe back to cover as quick as you can. This should give you an idea as to where they are hiding. Step out again, this time in single zoom, and locate one of the spots you saw and shoot. As soon as the shot is fired, seek cover again. You can repeat this quickly, and may be rather surprised by the results.
9) Corners. They are deadly. When crouched beside a corner, your knee pops out before the rest of you, giving away your position (useful against others, dangerous against you). Do not crouch around a corner. The same goes for walking... unless you must maintain absolute silence, break the walk and take a quick step around the corner for a peek. If enemies are there, they won't see you creep out part-by-part, and instead hopefully surprised by the quick movement.
10) Aiming. With the scout, it's best to aim (in this order): chin, upper chest, head, lower chest. The scout has a tendency to fire slightly above the crosshair.
11) Pack a set of grenades. A HE is useful for blowing away hiding people that you can't see. Smokes are good for blocking enemy vision, creating a hiding spot for you (I do not recommend hiding in smoke), or a get-away. Flashes can blind enemies so you can peek around corners, or (thrown at your feet or above you), will prove an effecient way to escape.
12) Don't be an idiot, and keep your sidearm handy.
13) Use cover to your best advantage. Whether it be ducking, poking around corners, or typical concealment... it is your best friend.
14) Know what can be shot through, and what cannot. An invaluable tool.
15) Don't be a moron and lead rushes. Don't run off to where you are no help whatsoever to your team. If you do this, COMMUNICATE... or I might have to knife your arse.
16) Teh knife. The most satisfying part of the game. Use it, abuse it, love it.
17) Repetition. Do not hide in the same place every time. Know the enemies' usual places, and if they repeat their hiding places, pop a cap in their ass.
18) Omfg scorz monger! You're not out for kills, you're out to help your team. Indicate enemy positions, whether a place is clear or not, clear an area for your team, etc.
19) Don't be Rambo. You're a sniper. Not Rambo. You can't even take off your shirt, or wear a bandana.
20) Teamwork. Teamwork! TEAMWORK! If you don't work with your team... leave.

That's all for now. If you want some more tips, give a holler.