Start by getting and installing good genealogy software. I strongly recommend starting with the "Personal Ancestral File" from FamilySearch.org. PAF is not only a very good genealogy program, it is also totally free. It is used by a huge number of researchers so tutorials, books, tip sites and user forums are plentiful if you want to learn the tricks of getting the most from it.
Click the first link in the Resources section to download PAF. After you install the program, open it and click "Getting Started Guide" in the Help menu. After you read that, you can plunge right into step 2 or you can go to the Lessons that are also accessible through Help.