Hi Polly,
Let the technician know that you're afraid of needles and ask him/her to help you out. If this is a case of "you've never had a blood test before" and you're just afraid of the unknown, ask them to explain what they are going to do. Then you can decide if you want to watch or be distracted.
If you've had blood tests or needle injections before and you have a history of panic, the tech absolutely needs to know that. They may decide to monitor your blood pressure before/after to make sure you're alright.
The test itself is really far less painful than menstrual cramps, so if you can handle those, this will be a walk in the park.
It's the needle that scares folks, so I have three suggestions:
a) don't watch
b) take along an iPod or something that you can listen to which will allow you to distract yourself while they're doing the procedure. Ask permission to use it since there will be other medical equipment in the lab and you don't want to interfere with anything. If they won't let you use the iPod, just ask someone to go into the room with you and talk to you while the tech is working.
c) take some juice and a snack bar or some granola with you. You won't really be losing much blood but some people feel a bit light-headed. Having something to boost your glucose levels will help overcome that.
The whole test takes less time than it takes to watch a tv commercial so it's really fast.
Good luck!