Start the ball rolling by asking your parents, grandparents, and other relatives about their parents, grandparents, great-grandparents, great-great-grandparents, and so on. Jot down as many details as you can, even the seemingly unimportant information like an occupation or hobby.
Specifically seek out full names, dates, and places to aid in your search. If your relatives immigrated to the United States, find out what country or, better yet, what city they came from. The more explicit information you have, the better.