Start with yourself.
What genealogical information do you have about yourself? Look at your birth certificate, milestones in your life (your wedding, births of children), photograph albums, and family heirlooms you may have inherited. What schools did you attend? How many different places have you lived? Is there other family information hiding in boxes in your attic, basement, or garage?
Expand to other family members.
Talk to as many of your living relatives as possible. Start with your parents and grandparents, then move on to aunts, uncles, and cousins. Ask them what they know about the family. Be on the lookout for stories that have been passed down about your ancestors. Who might have the family Bible, birth and death certificates or citizenship records of your immigrant ancestors? You never know unless you ask!
Explore online.
You've probably heard of Ancestry.com, but the website FamilySearch.org has many of the same records, and it's free. You will have to set up an account to take full advantage of everything that FamilySearch has to offer.
You also might be surprised by what you can find about your ancestors with a well-crafted Google search.