Ow, my ears!
The sniper rifle is lots of fun to use, but sometimes I wish you had the option of attaching a silencer to it. It's hard to feel stealthy when your shot is loud enough to wake anyone within five miles!
Keep the clip well stocked
Preferably have at least two shots in the clip before opening up on an enemy. The main reason is that you'll be able to quickly follow up with a second shot if necessary (while they're stunned); otherwise they might retreat behind cover before you can reload. A second reason is that otherwise, you'd go into an automatically reload because the clip emptied. That would take you out of your sniper view, possibly before you had time to see whether the enemy was killed or not.
Don't rush your shots. If the enemy is moving about, it can pay to watch their movements for a while so you can pick the best time to shoot (e.g. when a head is sideways on, giving the biggest target for a headshot; or when two enemies cross, giving you the potential for taking two down with one shot). I believe this is called 'patterning'. You're watching the enemy with the aim of exploiting any patterns of movement.
Aiming by moving
With any weapon, you can slightly adjust your aim by moving of course; typically left or right. Making small adjustments this way can be easier than trying to adjust your aim with the aiming joystick, and it's something you're probably doing a lot of the time without even thinking about it. I use this quite a bit with the plasma rifle at medium to long range. With the sniper rifle it seems particularly useful as you often only want very small adjustments, e.g. to pick off the next enemy in a distant group. You can just walk to the left or right a little.
This method can also be useful when attempting to use the rifle unzoomed, particularly if the enemy is moving and relatively close (e.g. an Elite within plasma rifle range). Use the aiming joystick to get the rifle pointing in the right general direction, then use movement to get the enemy drifting towards the tiny reticule. Staying calm, pull the trigger just at the right moment, and you've got a hit. It can be a lot easier than trying to track the enemy with the aiming joystick, which is rather clumsy with this weapon when unzoomed.
Don't bother firing at a covie vehicle, as sniper rounds appear to cause no damage whatsoever. Of course, with a Ghost you could always aim for the pilot however. That's different. If the Ghost is facing you, you can target his feet, which slightly stick out underneath.
When sniping an Elite, you might like to try hitting him somewhere other than the head to watch how he recoils appropriately - another fine example of Bungie's craft. It can be fun to torment an Elite like that; and if you weaken him enough without killing him, you can watch him charge at you from far away, and you can enjoy taking him down as you please.
A sniper's dream
For perhaps the best sniping in the game, let me recommend the twin bridges megabattle. It's a sniper's dream. But there are good opportunities in the rockslide megabattle and spiral path megabattle too.