Well, you would probably have to request IRS tax records and employment records and school records to show that they lived in the U.S. for a certain amount of time before you were born. If your father does not have enough time living in the U.S., it may be possible for you to use your grandfather's time in the U.S. If they were not born in the U.S., you can file a G-639 Freedom Of Information Act (FOIA) request and get a complete copy of their immigration file which should include the information that you seek. It is free but may take 2 to 3 months or more to process. Here is a link:
As far as the other evidence of physical presence, you may have to hire a private investigator to do the legwork or you, though you probably could contact the IRS and schools that they may have attended on your own.
As far as how much time they have to have had in the U.S. before you were born, take a look at this link on the 6th page:
Basically you have to prove your father lived in the U.S. for at least 10 years before you were born and at least 5 of those years had to have been after he turned 14. If your father did not have enough physical presence in the U.S. before you were born, you can use your grandfather's physical presence. Also, if your parents were not married at the time of your birth, you would have to show additional things. Here is a link:
If you can meet all the requirements and show proof, you should apply directly for a U.S. Passport.
My goal is to provide you with excellent service – if you feel you have received anything less, please reply back as I am happy to address follow-up questions and there is no additional charge. Also, should you need to chat on the phone, private email or need help reviewing documentation, I am happy to do so for a small additional cost. Let me know if you are interested in these – I am happy to give you more details! When we are done, if you would be so kind as to leave a positive rating for my service, I would sincerely ***** ***** You can do that by clicking on the 3rd, 4th or 5th stars if you see them, or the smiley faces if you see them. You can even ask additional questions without additional charge even after leaving a positive rating. Thank you for your understanding.