Start with your last known ancestor...usually great grandparent, you should know their birthdate and place of birth. You can call this town/city's clerk and request a copy of their birth certificate...this will list their parents names and places of birth, usually...you can go on from there....and so on and so on...it gets addictive!
You can go to state archives etc for research too...if feasible. They have birth/death/marriage/census records. LDS churches sometimes have family history libraries (mormon churches) and they have the ability to borrow records on micro fiche from Salt Lake City. They have the largest collection of family history records in the world...from all over the world!
I am from New England...there are many genealogy groups there to get information from. Also, some information is online. I have found ship's lists etc. online.
It is fun...if you have the time.