Write down everything you know about your family history. Begin with yourself and work backward to your parents and their parents. Search for documents that can verify family stories - birth certificates, military records, wills, marriage licenses, deeds, etc. Plan a family reunion or visit with relatives to obtain all the information you can. Look at genealogy books and find a simple beginner's handbook.
Some books contain genealogy software.
Purchase genealogy software. Most software companies offer free samples that you can download and test. Find the software that works best for you. Visit your local Latter-Day Saints Family History Center. Centers are located in most major cities and have a wealth of ancestral information.