Based upon the information you provided, you are likely acquired United States at birth. You could apply for a U.S. passport, which will be evidence of your citizenship. The evidence you would need to gather varies as it depends upon the type of evidence you can obtain. You would need to gather documents such as your birth certificate, your parents' marriage certificate, proof your father was a United States at the time of your birth, proof your father was a United States citizen, and evidence your father residing in the United States as required.
I agree with my colleague here. it is very likely that you actually did acquire your USC at birth and should most definitely explore the issue further. At the same time, you belong to a category of individuals who would benefit a great deal from consulting an immigration attorney in order to make sure that you did.
I agree that you very likely acquired your citizenship at birth depending on the timing of your birth. You should contact an imimgraiton lawyer to help you with the process of appying for formal recognition of your citizenship. If you have a few questions, feel free to call me at 216-338-2120. I can answer a few questions without charging you.
You should always consult with an experienced immigration attorney to make certain that the advice you received is appropriate for your particular immigration case.