Even when sniping, never stay in one spot for long. Someone will spot you and flank you.
Don't go to the "sniper" areas (rooftops, the silo things, catwalks), it's the first place anyone looks when they see/hear/feel a sniper shot. Instead, look for deformities and hills in the terrain to hide by. If you're PAC, hide in shadow; your dark armor will make you very hard to see.
Most of the time, just wait until your target stops to kill them. It's rarely worth the chance of giving away your position to try and hit a moving target. There are some exceptions to this and you'll see those when they arise. Those shots that you just KNOW you can make.
When you see someone and aim at them, remember the military acronym: BRASS (Breathe, Relax, Aim, Sight, Squeeze). Take your time for each shot and make it count.