1. Sniper Rifle (Primary)
2. Sub Machine Gun (Secondary)
3. Machete Blade (Melee)
Your main goal as a Sniper is obviously to snipe people from behind the back, but it's the targets you choose that make the difference. Your number one target, as in all PvP games, is the Medic (healer). After a couple of minutes of healing a Medic will get a 10 second invulnerability (think Paladin bubble), this means you want to take them out before their invulnerability is charged and ready to be used.
With your sniper rifle equipped, right click to zoom in. You will notice a meter in the middle of your screen charging up. This meter determines how strong the shot will be, but you don't have to wait for it to be full to take a shot (although it is advised).
The best method is to take a vantage cover point and zoom in from behind that cover. Your cross hairs will be zoomed in on the box you're crouching behind, but that is ok, you are only charging to full capacity. Once you are charged, side strafe out from behind your cover, but don't take the shot, just notice where everyone is and go back to cover. Now that you have a mental picture of everyone's location, pop back out and take a shot at someone you noticed before, and always aim for the head, always! Whether you miss or get the shot, immediately side strafe back into your cover and let the gun charge again. Rinse and repeat this method.
On some of the larger maps it is possible to snipe engineer gun turrets, and these are just as important as Medics when choosing targets. They will take a few shots to take out, but most engineers are only concerned with Spies and are oblivious to snipe attacks against their turrets. The same applies to all engineer items, but turrets are more important.
Listen for the Spy calls and take note. If you hear your team call out that their Spy is disguised as a Soldier, then start taking pop shots at every Soldier from your team since you usually have a better view then the people in the fray of things. I've taken out a ton of Spies like this.
Lastly, If you get charged you always have your secondary sub machine gun, and your melee machete knife. These are both substantial backup weapons, but as with any class if you aren't using your main weapons you aren't playing to your strengths. If you find yourself just using the sub machine gun over the rifle, then just switch to the Heavy class, as that is automatic weaponry at it's best.
Now get out there and pretend you're Mark Walberg in the movie Shooter, or Gallagher with some watermelons if Marky Mark isn't your thing.