It hurts a bit, but it shouldn't hurt intolerably. I'm always nervous even though I've done it several times and survived. (I promise I'm not typing from the afterlife. ;))
If you clench your fist and arm, and look at the inside of your arm just below your elbow, and you can see a vein bulging a bit and holding steady, that's a good sign that they'll be able to get at your blood easily and without too much pain. It isn't very significant if you can't, though -- you might have an accessible and well-behaved vein that just won't bulge under those conditions. (Mine show up as well as they do partly because I'm kind of pale and have skinny arms.)
If you're going to give blood, it's a good idea to prepare your body ahead of time. This is especially important if you're small, because smaller people are giving away a larger proportion of their blood. Drink plenty of fluids -- that's very important. Eat well ahead of time: you don't want to have an overfull or upset stomach while you're lying back, but you don't want to be hungry either because if your blood sugar is low you won't feel as well during the process. Ideally, you'll have eaten a substantial meal a few hours ahead of time and digested it so that the nutrients are in your bloodstream instead of your stomach. Also, this might help you feel less nervous.
For women, it can be helpful to avoid donating blood immediately before or after a period. You may be more sensitive to pain shortly beforehand, and your iron might be low right afterward. I try to donate during the middle two weeks.
Some people donate blood and feel fine the whole time. Some people are literally nervous enough to become dizzy or throw up before they even get started. Some have varying degrees of physiological reaction to the process, either the blood loss or a reaction to the needle itself -- not because of extreme fear or pain, your body really does react to having a vein punctured! This is nothing to be ashamed of, though it is uncomfortable. It might not be a very strong reaction for you at all, but if it is, you'll still be okay.
If you feel shaky, dizzy, etc., for any reason, then it may help to sip a cold drink (I find a clear soda works well) and to have something cold placed on your forehead or neck. Most of the local blood donation people here are very solicitous and helpful, willing to do a few extra things for a wobbly but determined donor. I hope yours will be just as nice.
Personally, I felt very dizzy throughout my first time donating blood. I have gone several times since then and felt much less dizzy during most of the process, except for the one time I meant to go before lunch and wound up going around 4PM without having eaten. Yes, I passed out. Don't do that, it was stupid. :P