The best place to start is to ask all your current relatives what they know about your family tree. Information about your relatives can also be found written into family bibles or other family records, like birth certificates, death certificates, military records. The web can provide a wealth of answers - start with ancestry.com
A computer genealogy program can help you to collect the information. I find Family Tree Maker to be quite helpful. The Church of Latter Day Saints can also be helpful - they run family history libraries in many countries around the world.
pgorman