how can I get my name added to my sons birth certificate
I don't know where you live, but you just need to get an amendment specifically to declare paternity or one to change paternity if there is already a father listed on the certificate. A paternity test will only prove if you are the father, not put you on his certificate. It can take up to 12 months, but after the state seals the original and makes a new one. You can also change his last name to yours, if his mother agrees, with the same peice of paper. There is also a fee involved, but I only had to pay $20.
you have to take a DNA test and then take those results to your county court house. They should be able to fix that in no time.