I''m a wuss when it comes to having blood drawn. I admit it. So, when I have bloodwork, I ask for a "butterfly" needle, which is a very small one -- the smallest they can use to draw blood. I have good veins, so getting out one of the kebab skewers isn't necessary.
I have found that never seeing the needle is a good way for me to approach an injection or getting blood drawn. I close my eyes the whole time. As I said, I'm a wuss and a big baby about it, even though I have to have bloodwork three or four times a year. That's just how I have to get through it.