Relax. Being physically tense makes everything more uncomfortable because your body literally becomes more rigid, which makes it harder for the needle to go in or the cuff to tighten.
I also find that I prefer to watch the needle go in for both the fingerstick and the arm stick so it can't "surprise" me, but I've never known anyone else with that preference.
Know your sensitivities before donating. I'm reactive hypoglycemic, so I can't just eat cookies or ice cream before or after - I'll pass out. I usually try to donate after a nice serving of protein, preferably a steak. Avoid anything that could make you queasy, including a really huge meal - I literally eat just a steak. I shouldn't have to say this, but don't drink alcohol directly beforehand!
If you have difficult veins, it's a good idea to wear a loosefitting short-sleeved shirt, like a baggy tee, so that your clothing doesn't get in the way. On that note, don't think they don't want you to come in just because you have difficult veins. Also, don't assume that you have difficult veins - sometimes all it takes is a really talented lab tech.
It's better to make an appointment if possible, because people are more generous than you might expect, and there can be a long wait for dropins.
Remember to only give to the Red Cross, Canadian Blood Services, or another nonprofit organization! If anyone is going to profit off your blood, it should be you!