Fill out a pedigree chart to the best of your ability. You can download these forms from the internet.
Contact older relatives to try to fill in information that is missing on your pedigree chart. Get as much information on your family as you can from these precious resourses because they won't be around forever. I have a friend that asked her grandmother for help with her genealogy and her grandmother said she would, but she died during the night. They will be so happy to talk to you about their past and the people they knew long ago. Try to tape them if at all possible for two reasons. The first is so you can go back and make sure you get the information right and the other is the priceless recording you make of your relative's voice.
Now the fun begins. Decide which line you want to follow and begin looking for information on that line. I suggest taking what you know and searching for your names on RootsWeb.com. This is a free site and many people have added their genealogy to the site. You can contact the people who have submitted the information through e-mail. Their e-mail address is with the information in a grayed out area that is hard to read.
Another good place to start is FamilySearch.org and if you are having problems a Family History Center is a good place to go ask questions. There is a Family History Center locator on the website. They have some good how-to information and aids on the site. Ancestry.com is also good, but isn't free. You can join for $10 a month.
Document EVERYTHING. Keep a record of where you've searched so you don't keep searching the same records for the same information. I'll go into documentation in more detail in another post.
Just keep following leads, and when you come to a dead end for the moment with the first line you chose, start with your next line.
Good luck with your hunt.
Dale L. Edwards