First, if you were born in the United States, you became a citizen of the U.S. at birth. Your birth certificate, issued by the state government that you were born in, is your proof of citizenship.
If you were naturalized in the U.S., your naturalization certificate is your proof of citizenship.
If you were born outside of the territorial United States and you have a right to U.S. citizenship through your parents, you will need to apply for a U.S. passport in order to obtain proof of citizenship.
If you were born outside the United States to U.S. citizen parents, youi can apply for a passport the same way a person born in the U.S. would, but there are a few extra steps. You will need proof of your parents citizenship, proof that your parents abided by with any applicable U.S. residency requirements, evidence that you fulfilled any residency requirements (or proof that you were excused from doing so because you were not aware about that law). Passports are available at any U.S. consulates abroad or from passport offices in the United States. It is strongly recommended that you apply for one at a consulate.