Q. How can I find some information about biographical influences on Tennessee Williams's The Glass Menagerie?

The best place to find this information will be in the library literary criticism databases.  

In Gale Literature Resource Center, click on "Works Search" on the top right of the screen.  Search for The Glass Menagerie.  Click on the result by Tennessee Williams.  At the top under "Showing Results For" you will see links for literature criticism on the story (39), links for biographies on Williams (3) with information relating to his various works, topic & work overviews (4) and primary sources (4).  These links should give you some of the information you are seeking.

You can do a search in the other criticism databases for "Tennessee Williams" AND "The Glass Menagerie" to go through other articles relating to him and the story.