I don't really mind needles, but I'm no good with blood, and I know at some point afterwards (usually 5 or 10 minutes), I will get really faint. I warned the midwife that I tend to get dizzy and faint, and I'd be better lying down. Usually I find blood tests painful, it feels like a hard pinch the whole time, but this time I hardly felt anything. I had drunk a lot of water to help with the scan, and like a pp said, you have more blood in your body during pregnancy. My DH was in the room too, so the 3 of us were talking and laughing. It did take a little while as I needed some extra vials taken, but it was still probably only 2 or 3 minutes total, if that. I did go dizzy after, but I knew it was going to happen, I'd warned the MW, and so we were prepared. She also apologised and said there would probably be a fair bruise, as she'd had to take so much, but there was no pain after and a small red patch over the vein for a day or so afterwards, but not a huge purple bruise like I'd been expecting!.
It's not fun, no-one likes blood tests, but it's not usually too bad. Tell whoever is taking the sample of your fears, like others have said, keep hydrated and warm, it makes it easier to find a vein. Midwives especially are really good at taking blood, as it's something all pregnant women have to have done, and a lot of us aren't too good about it! They are usually very chatty and are able to put you at your ease, so good luck, and I hope it all goes well for you :)