I consider myself a decent sniper, but when I go into Crucible, I'm wrecked beyond belief. There are guys who headshot me the very second they scope in. It's -blam!-ing ridiculous! I don't understand how they do it!
EDIT: A lot of people are saying that they get their skill from Halo. However, I actually snipe very well in Halo, but not-so-well in Destiny.
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Run your rectile into your target and shoot. Dont worry about the right thumbstick as much. But dont strafe in a pattern because the other guy will take notice and keep his rectile in one spot ready to shoot while you run into it. The hidden hand perk works wonders as well.