How do I add my child's father's name to her birth certificate?

When was the child born? Try going to the local county clerk or hall of records to see what's necessary.

How old is there child, or is the child born already ? And where is this, county and if in the US what state. Is the father signing to be put on it ?

First there are many questions to be asked.
What state are you in?
Are you and the father married?
Does the father acknowledge paternity?
In Texas... where I'm from...
If you are not married but the father knows he is the father... all you need to do is have him sign a avadavit of paternity(notorized) and then they can ad him at the records department in your county.