How do I find the owner of a found Birth Certificate?

with a name and a date of birth almost anyone can be found, as long as they are using that name; since it is found property, your local police should be willing to accept the document as found property (particularly due to the potential for fraudulent use)

If not, the state agency issuing birth certificates may accept it; if not, destruction of the document would probably do no harm, since the person could obtain a copy from the state agency if needed

any Priv Invest would have access to databases that could locate the person, but it would normally involve a charge for use of the commercial database

You may advertise through different media channels to find the owner of that birth certificate.

Give it to the police and let them find the person. They have computer programs that do that kind of thing.

Post the name and birthplace in Facebook or do a search.