You should look at the resolved questions. Either browse them or use the advanced search at least three times, for the words
Free family tree
free family history
free ancestry
People ask the same basic question, "How can I find my family tree, for free?" 3 - 14 times a day here. All of us top 10 have stock answers. After 2 - 4 of us paste our stock answer, the rest don't bother. All the stock answers are well worth reading. All of us are warm, wise, witty, well-read and, above all, devilishly handsome. We have quite a bit of overlap on our favorite links, but we emphasize different aspects of the hunt in our advice.
Here is my stock answer:
There are over 400,000 free genealogy sites. Among them (without http://)
www.cyndislist.com - 250,000 links, all categorized.
www.familysearch.org - The Mormons. Gazillions of records.
wc.rootsweb.ancestry.com - Roots Web World Connect - 600,000,000+ entries
usgenweb.org - Sites for every county in every state in the USA
vitals.rootsweb.ancestry.com/ca/death/ - California Death Index, 9,366,786 records
www.findagrave.com - 83 million records
genforum.genealogy.com - Query boards for every county in every state, and thousands of surnames.
boards.ancestry.com - The other Query board site; counties and surnames too.
archiver.rootsweb.ancestry.com Roots Web Mailing List Archive - Over 30 million messages
I have a page with real links to all of those, but you'll have to wade through some advice and warnings first.
If you didn't mention a country, and you didn't go into Yahoo! by one of their international sub-sites, we can't tell if you are in the USA, UK, Canada or Australia. I'm in the USA and my links are for it.
If you are in the USA,
AND most of your ancestors were in the USA,
AND you can get to a library or FHC with census access,
AND you are white
Then you can get most of your ancestors who were alive in 1850 with 100 - 300 hours of research. You can only get to 1870 if you are black, sadly. Many people stop reading here and pick another hobby.
No web site is going to tell you how your great grandparents decorated the Christmas tree with ornaments cut from tin foil during the depression, how Great Uncle Elmer wooed his wife with a banjo, or how Uncle John paid his way through college in the 1960's by smuggling herbs. Talk to your living relatives before it is too late.
You won't find living people on genealogy sites. You'll have to get back to people living in 1930 or so by talking to relatives, looking up obituaries and so forth.
Finally, not everything you read on the internet is true. You have to be cautious and look at people's sources. Cross-check and verify.
So much for the warnings. Here is the main link.
http://www.tedpack.org/yagenlinks.html
That page has links, plus tips and hints on how to use the sites, for a dozen huge free sites. Having one link here in the answer and a dozen links on my personal site gets around two problems. First, Y!A limits us to 10 links in an answer. Second, if one or more of the links are popular, I get "We're taking a breather" when I try to post the answer. This is a bug introduced sometime in August 2008 with the "new look".
You will need the tips. Just for instance, most beginners either put too much data into the RWWC query page, or they mistake the Ancestry ads at the top for the query form. I used to teach a class on Internet Genealogy at the library. I watched the mistakes beginners made. The query forms on the sites are tricky.
If you've read this far,
And you are still interested
And your ancestors were in the USA by 1930
And you know the names of at least two people (husband and wife, parent and child) who were living in the same house in 1930
I'll look for them in the 1930 census to give you a start.
Write to me via my profile.