Depends on which one your getting, you can get one before you conceive and they put a needle through your stomach and collect fluids around the baby and that should contain you and the baby's fathers DNA.. 1% changes of having a miscarriage... I'm doing this soon. 

If you're willing to wait, they can do one at the hospital when you have your baby.

You can go through your local court as well for a court ordered one. It's just a paper you fill out. (I live in CA).

Call your states DHHS (or whatever human services in your area) sometimes they will direct you how to get one, or possibly pay for it if you are seeking state benefits.