I'd advise you to talk to the oldest relative you have and find out as many of their ancestors as they can remember. If you can find people who lived in the nineteenth century (1850 or so is ideal), you might have success finding them on rootsweb.com. Someone in your family might even have done some genealogy work!

You don't say whether your ancestors came from the US or other countries. The US information is extensive, but there are other sites to find information for the UK, for Europe, and other places. rootsweb is a free site. 

See if your family has any old Bibles where they have recorded births and deaths. you might even find some old names you never heard of. If one of them married someone else, there's a chance that they might be part of someone else's family tree.

You can also try getting information from the Social Security system. There is a Social Security Death Index at rootsweb.com, where you can enter the name of an ancestor or relative who has passed away. You can view the available information online, free. Then you can request information from their original application. You can also obtain death certificates from county officials if you know where your relative died, which the SSDI may help you find out too.

Try Cyndi's List, here: http://www.cyndislist.com/

You can even try searching for names in a search engine. The best thing is to get the full name of someone born before 1900 and entering it in quotes, like this: "John James Smith". 

Good luck!