A good bet is to start with the oldest living relative you can get your hands on - a grandparent, great aunt or uncle, something along those lines. My dad went through a phase last year where he researched the hell out of our family...his mom had a good amount of stuff. Things worked good for him, because most of his relatives came from one small town. If that's the case with you, then you can probably get a lot of records from that town. Quite often an amateur historian will write a book about their county's founding and the original families that lived there. So, again, if you can find out where they lived, try to find any records or books dealing with that time period.
Genealogy is a really time-consuming hobby...unless an earlier relative recorded a lot of stuff, you may be out of luck.
There are also companies who will get information for you, for a price of course. I don't know which ones my dad used, but you could probably just search for 'genealogy' on google.