A lot of different techniques work for different people, for me, what I do is:
1. Take a long breath and let it out slowly. I close my eyes and get comfortable, then let all my muscles relax.
2. I focus on the needle. For some reason if I look away, I don't expect it so I flinch, and it hurts.
But the most important thing is to be relaxed - if your muscles and tendons are lax, it won't create as much of a shock to you.
Also, the needles to withdraw blood are rubber, and very small in gauge.