Which game?
Free Step Dodge
ninemil
Pictured Mind
Depends. Every sniper is different. Every game is different too.
Hazard
For any game, it's gonna require you to aim ahead of the other player if they're running. Don't try to track them with the crosshair, cause you're gonna have a bad day.
His Reverence
Find a corner, brew a nice cup of coffee and grab some snacks. Sit back and maybe, MAYBE, you'll get to press the trigger a few times.
Pictured Mind
Rev's strat works best when you're playing Destiny and you have ice breaker. Free bullets.
Otsu
If its Advanced Warfare, dont ever snipe because they fly around everywhere and dont stop and you cant get a shot and then you have to spray your secondary and then you run outta ammo and have to run for the gawds
Dr Snipe
Sniper Elite is a good simulator and you can also turn all that off and shoot like a FPS.
Pictured Mind
^ While in Halo that is a very good strat, in Destiny is sucks.
Radiance
One thing that's helped me is toning down the sensitivity in Halo, the rest seems to be mostly just practice.