How do you find out about your Jewish lineage if you only have very limited information (ex a place of birth, grandfather’s name?)
Nice timing, Terri!
A couple of weeks ago I was given a pile of books, and in it was one called Finding Our Fathers: A Guidebook to Jewish Genealogy by Dan Rottenberg. It has step by step instructions for finding out information about your Jewish relatives. It also has a list of over 2000 Jewish names in the back, with information about what families are related to them, places of origin, etc. I'll summarize a bit from this book as my answer:
First of all, arm yourself with a notebook. Prepare a simple family tree, and fill in all the names you can as far back as you can. A good way to get starting information is to locate elderly relatives and talk to them. One of them might just have your information. If they don't, they will surely help you fill in your tree with some names of your forbears. You have a birth date - if he's not still living somewhere, do you know where he did live, or where he's buried? Visiting graves can give you more information, sometimes a lot more if several generations are buried there. At the least, you will have his and his father's Hebrew names to work with after the visit.
Back to finding information on just your grandfather--did he live in the United States? If he did, and you found approximately where he lived, you can start by researching online census information. Ancestry.com gives you some access without having to subscribe. The National Archives' site http://www.archives.gov has step by step instructions on Census records, as well as other good information, such as ship passenger lists. You can also look for birth, death, and marriage information in the public records of the location he lived. If he wasn't born in the US, you can get information about him in the public records of the country he was born in. If they still exist, the synagogues and other Jewish institutions near his birthplace also might have good information.
Hopefully, this answer can get you started. The book gives plenty of other sources for information, such as Jewish libraries and archives in the US(American Jewish Archives, American Jewish Historical Society, YIVO Institute, etc) and worldwide, for the generations when your family was...wherever it was. Happy hunting!