Cyndi's List of Genealogy Sites on the Internet is an excellent collection of links, well organized and maintained.Learn about the Family History Library and find a local Family History Center.
There are several software packages for genealogy. I've been using Family Tree Maker.
Ohio and Pennsylvania are my primary US research locales:
In the 1700s, several of my ancestors lived in Maryland
Susan K. Hahn's home page or family history extracts