First of all, remember that you are not alone in your anxiety. It has been estimated that around 10% of the population have an undue fear of needles.
Second, tell whoever is drawing blood from you that you have a phobia of needles... they may well be able to administer a topical (local) anaesthetic... this can be surprisingly effective... you could perhaps ensure that your feet are elevated, to minimise the vasovagal response.
Third... don't look... look anywhere but at the site where blood is to be drawn.
Fourth... remember to consciously force yourself to breathe slowly and deeply... breathing shallowly/rapidly can exacerbate the onset of panic.
Fifth... try to keep in mind that there are literally millions of venapunctures daily across the world, and the number of bad side effects is negligable.
Sixth.... Try to focus on just how good you will feel with yourself once you have gone through it!
Good luck, and remember think calm thoughts, and breathe slowly and deeply.