OK, maybe you don't have a family tree, but the family believes that it goes "way back" or you think it might because you don't know for a fact that all your ancestors came to this country recently.  Where to start?

FAMILY ARCHIVES: Interview the older members of your family to see what they know the names of their forebears and the dates and places of their births, marriages, and deaths.   If your grandmother knows the name of her grandmother, you can write a family tree going back five generations.  This will get you into the mid-1800s.

Older relatives may also have documents or scrapbooks that show the names of ancestors and the dates they were born, got married, and died, deeds, wills, etc.   Family bibles may be acceptable as documentation, and they are valuable because they often list many generations.  Be sure to copy the page that lists the publisher and the date of publication.  These items are often thrown out (when the owner dies) by descendants who do not realize the value of keeping such documents.   Try to get the originals or copies into a safe place while there is yet time.   Also, get a copy for your files.  

NOTE:  The SAR does not require certified copies of these documents; "xerox" copies are satisfactory.

FAMILY HISTORIES are available for many surnames (your family name, the Smith of John Smith).  These are available at genealogical or historical libraries, college and public libraries, and lineage society libraries.  Except for the lineage societies, libraries generally cover only families in the local area.   The Library of Congress has a huge collection of family histories and publishes an index which is available in many large libraries.  

NOTE:   When you copy pages from a book, be sure to also copy the title page and see that it contains the title, publisher, city of publication, and date of publication.   Sometimes you have to copy two pages to get all this.