Mary, the easiest way is to interview to your grandma or a great Aunt. If you can get the "oral" family tree dating back to 100 years, with birthdays, dates of death, marriage dates, and maiden names, you will be able to track the rest from online records. Most online records won't give you information on living people, that's why getting that first hundred years of information is important.
Getting the first hundred years is not as hard as it sounds, that's three generations at most. What was grandma's mother's maiden name, and when did she get married? What were her siblings names and what was their birth order? Stuff like that. Mother's maiden names is important, because that is the only way you can track their genealogy.
After that, searching on line is a breeze. You can even take advantage of another cult's obsession, LDS family records, very handy!
http://www.familysearch.org/
A grandchild should interview their oldest living relatives at least once. Unless of course, that relative is an axe-murdering abusive freak. First of all, you are getting invaluable family history. Second, you are providing a pleasant diversion for a senior citizen, who is usually more than eager to share forgotten memories.
