Get Online
With a quick online search, you can find a wealth of free genealogy Web sites and links. These can direct you to numerous databases for various states' information, old records, archived history, etc. These free genealogy sites can give you invaluable tips for your search as well.
Almost all are run by volunteers, so if you grow to love the site, you may decide to get further involved and volunteer yourself. And remember, they offer free genealogy so they have to get their revenue from somewhere. (Ahem! donations.) So you may even decide to drop them a little something, it doesn't defeat the purpose of “free genealogy,” it simply helps them continue to provide their services.
Check the Census
Again, online records are a great resource. The Census Bureau has records going back to the late 1700s for some states. Of course, these public records are a great way of finding genealogy. You may have to do some digging, though.
Go Military
This form of genealogy research can be tedious, but is exciting. You can go through old military records and find ancestors who served in various wars, in different battles, and sometimes even discover stories about their actions in war.
Links to military records can be found through online free resources, then you can take leads and go from there.
Man and Wife
Other public records that can be found online or through different old courthouse records are marriage licenses. This form of free genealogy can give you information on your ancestors, their marriage date and where they were married.
Sob Story . . . Or Not
Search out obituaries. Obituaries are free resources which will give you information on birth, death, and hopefully extra information about your ancestor's life and his or her survivors or those who preceded him or her in death.
Get Religious
Look for old church records. These can be the most complete form of free genealogy you can find. Churches continue to keep some of the most complete records of parishioners you will be able to find anywhere.
In church records, you could hit the jackpot in free genealogy research. You could find birth dates, death dates, marriage and family information as well as other vital statistics. Church records may be somewhat difficult to find, but with some online searching, you can get some good leads and find help.
LDS Family History Centers
The LDS Family History Centers are huge repositories of free genealogy for use by the general public. Either look up the centers online or in the phone book to find one in your community.
In LDS Family History Centers, you can look up free information on your ancestors and find further leads through the center's extensive database and the help of the genealogy librarians.
Check It Out
Head down to your public library. Public libraries are outfitted with banks of free genealogy for your use.
Go to the reference desk and ask for a tour of their free genealogy references before you start. Each library's policies and databases are a little different. The reference librarian will be able to help you get started and will be able to help you if you run into any snags.