Don't drink and dive
As tempting as it might be, avoid the urge to "calm your nerves" with a few drinks (especially anything high gravity) or any kind of self-medication. Many, if not all, skydiving facilities make you sign a waiver beforehand promising you haven't done any drugs or had anything to drink recently. If you break the rules, they won't let you jump.
And although you might be able to fool them, you should be as lucid as possible just so, you know, you don't miss directions, screw something up, and jeopardize your life and the lives of everyone else diving out of a plane from several thousand feet.
Save the drinks for after your "Welcome Back to Earth" celebration. There will be plenty.
Don't give in to fear
I am a coward. I HATE roller coasters, heights freak me out in general, and the few times I've ever gone faster than 100mph in a car were completely against my will. So naturally, the combination of heights and extreme speed should have given me the vapors and had me blacking out the second I was out of the plane. But it didn't.
The truth is, you don't really have a perception of being thousands of feet in the air when you're free falling. The hazy ground below doesn't appear to get any closer for much of the fall, and despite actually reaching speeds around 120mph (terminal velocity), you don't have stationary marks in the sky as reference points. It is the sky, after all. Your brain just thinks you're basically floating with a super-strong fan blowing air in your face. Kinda like a Magic Eye, but with a lot more danger and a lot less eye-crossing.
Once the chute opens, you're much more conscious about how high up you are, but the scariest part is already over.