Start with yourself and work backward in time: Begin with yourself and continuing with your parents and grandparents fill in as much information as possible. Interview family members and examine all documents such as family Bibles, wills, property deeds, photographs, letters, birth certificates and military discharge papers. Never start with a supposed ancestor and work forward.
Use the library resources. Use the library’s ON-LINE CATALOG to search for material located in the library.
Always try to find primary sources. Indexers, authors and abstracters inevitably make mistakes. Whenever possible, look at original wills, deeds, birth certificates and other documents, or copies of them on microfilm.
Beware the common pitfalls of research. Think of ways your surname could be misspelled, then search under those spellings. Remember that boundaries and names of counties sometimes change. In recalling where they lived years ago, relatives may name the nearest big city rather than the actual locale, or say the name of the county seat when they mean to name the county. Study the ways various documents are organized before you try to use them.
Keep careful records. Whenever possible, make photocopies of documents. Always record titles and dates of your sources.
Expect to visit many libraries and archives and to use many types of tools. No single collection will hold every document that you need. Likewise, no single source will answer all your questions. You will eventually use most of the tools of the genealogist: census records, deeds, county histories, wills, death certificates, etc.
More information can be found at Advanced Geneaology.