To a large degree, it really depends on what you already know. I think the free resources aren't as good as they used to be. Rootsweb used to be pretty good, but it was bought out by ancestry. If you don't mind giving them your credit card number, the free trials on ancestry can usually provide quite a bit of solid info.
I had a little bit of luck with familysearch.org which, I believe, is an LDS site. A lot of what you find through them, though, takes you off to paywalls somewhere else if I remember correctly.
There are other free resources that can be quite useful if you have specific things you are looking for (military service records, land titles, etc.)