Problem with blood test (help)

My problem is the actual process of taking the blood. I felt very sick, dizzy, and almost fainted when they were drawing the blood. There was barely enough blood to do the test. I know that they will need more blood than that in upcoming tests they do at my next visit in a few weeks. 

Does anyone have any tips to make it easier for me to let them take blood without passing out? 

I wasn't watching them do it. I was distracting myself on my phone and the nurse was talking to me. But that still didn't work.  I almost fell out of my seat. She had to stop and not take as much as she should have. This has happens every time I have had blood taken.