Visit your local public library. Most libraries will have a local history & genealogy section. Many offer free courses, usually in conjunction with a local genealogical society, in how to trace your ancestors. Your local genealogical society may also have a library (usually for members) with resources.

While the online sites are easy and available, I wouldn't become to dependent on them. Verify your sources and document, document, document. Genealogists are generally very friendly people, but do not suffer fools. (not meaning that towards you, but in general) As MacFarkus mentioned, talk to relatives -- they may already have information you might not know about. Always start with yourself and work back.

The Internet has certainly made genealogical research easier in some regards, especially in terms of networking, but most of the work is still found "in the trenches" -- dusty archives, information files, microfilm -- it can be tedious and frustrating, but rewarding as well. Don't be afraid to roll up your sleeves and get dirty!

Regards,

Todd