How can I get child support if the father is not on birth certificate?

You bring a paternity action.  Rarely is the non-custodial parent on the birth certificate in our practice.  Either there is a Recognition of Parentage (ROP), a consent, or a determination of parentage.  You will find the child support people at the county level are usually very helpful.  If you are receiving government assistance, the county will help.  Or you can go it on your own or use a lawyer.  I don't suggest doing it on your own, and not just because that is how we make our livening.  I do it because it is not always as simple as you may think.