Step-1 : Basic
Assuming you're level 4, start by creating your class. There are two basic types of snipers: Camp snipers and Mobile snipers. You can use whatever strategy you want, but these two categories are the mamma and pappa of snipers.
Step-2 : CAMP SNIPING
The camper knows all of the maps and their sniping positions so, first things first, know where to go based on the position of friendlys (and enemies if you've got a UAV). Most often campers will sprint to their spot, lay claymores, and then start shooting.
That's fine if that's the sniper you want to be. But for those looking for a little more stealth and subtlty, start the game sprinting from cover to cover. Once your in a position you know are hot spots for infantry or enemy snipers, crouch, or even crawl to get to your favorable position undetected.
If you run into an enemy undected, knife him, no matter how tempting it may be to get a head shot (this is to remain unknown). This is a great strategy for getting behind enemy lines.
If you are spotted along the way, you're either screwed or you have someone that knows where you are when they respawn.
Step-3 : CAMPING WEAPONS AND PERKS
Bolt action snipers (M40A3 and R700) are highly recommended for campers.
This is due mainly to the one-shot-kill damage stat. Some may say the .50 cal is good for camping, too, (one shot kill as well) but the ability to interupt your reloads to snag an extra kill is highly useful, and the .50 cal reloads SLOWLY. Which sniper you use is up to you, the M40A3 has one more bullet but the R700 (supposedly) does more damage.
PERKS : For traditional campers, perk one should be claymores, perk two should be stopping power (normal match), or sleight of hand or UAV jammer (hardcore), and perk 3 should be iron lungs or deep impact.
For stealth campers, perk one should be bandolier or claymores (recommended when sniping in buildings), perk two should be UAV jammer (hardcore) or stopping power (normal match), and perk three should be iron lungs for beginners and dead silence once you're experienced and into higher levels.
Step-4 : MOBILE SNIPERS
Mobile snipers keep their enemies on their toes. They find a spot, take one or two shots, and move on. Moving stealthily is recommended so you won't be followed. If you become exposed while in a spot, move immediatly. The goal of mobile snipers is to cause confusion and keeping deaths to below 5.
This type of sniping takes more practice and is generally harder than camping, so don't get dissapointed if you do bad your first couple times. Practicing in private matches with friends can be very helpful.
Step-5 : MOBILE SNIPERS' WEAPONS AND PERKS
Semi-Auto snipers such as the M21, Dragonuv, and Barret .50 cal are the tools of the mobile sniper. They are one-shot-kills in hardcore, have larger clips, and are much more useful when you run into an enemy unexpectedly.
At lower levels, the M21 has little to nada recoil, but the Dragonuv (supposedly) does more damage. Once you get it, always use the .50 cal, as it is a one shot kill, though the reload is slow.
PERKS : Perk one should be bandolier or 3 frags, claymores are unnecessary because you will be moving around a lot, perk two should be stopping power (normal match) or UAV jammer (hardcore), and perk three should be extreme conditioning or dead silence.
Weapon details :
M40A3
Pros: High Power and Accuracy, Low Recoil
M21 - Recommended for Hardcore Variants
Pros: Semi-Auto, Good Accuracy, Low Recoil, Can be used in CQB situations.
Cons: Low-Medium Power, Most players will become agitated upon being killed by the M21
Dragunov
Pros: Semi-Auto, Medium-High Power
Cons: High Recoil
R700
Pros: High Power and Accuracy
Cons: Medium-High Recoil, 4 bullet magazine compared to 5 on the M40A3
Barrett .50cal
Pros: Semi-Auto, High Power, Large magazine, Looks and sounds cool
Cons: Low-Medium Recoil
Warning :
-Sniping on a map such as Vacant or Killhouse is generally not recommended. However a experienced sniper can easily get many kills scoping at close ranges. Somewhat recommended for Search and Destroy.
-Remember your a sniper, not a commando.