You can also go to the National Archives. There is one in almost every large city. We have one here in Seattle, but I've only been there once. The internet has been the best source for me.
I do agree that talking to family is the best place to start. I found most of what I eventually got by using family records, and then searching on the names of my great great great grandparents. There are literally hundreds of descendants of that couple, and many of them have already done research. Our ancestors were Quakers and they kept detailed records, so I already had my father's data back to the first one who came here from England in 1720. From there it was a piece of cake.
My mother's ancestry is the Strong family and there was a wealth of information on them because they were a prominent colonial family. Very easy to research them.
My grandmother's mother's maiden name was Smith. I groaned when I learned that, but found all of them back to the 1500's online. Fortunately they were not the Joseph Smith branch.
It's so much fun finding the clues, and following them and finding a real nugget!
For anyone who is interested, this is my family genealogy website. http://home.earthlink.net/~herblst I built it myself.