Hi Bessie. Welcome to the world of genealogy - warning, it is addictive!
Your best bet, at this point, is to order your grandfather's birth certificate from the Massachusetts State Archives. I don't know whether or not they will give it to you; they may require proof that you are related (i.e., your father's birth certificate and yours, to show the family line).
Link to Massachusetts Vital records That link has a phone number you can call to see if you can order the record. There is a fee.
The birth certificate will give you at least his mother's name. According to the MA Birth Index on ancestry.com, his birth record can be found in Vol 6, Page 373
I checked the 1940 census. The only Joseph Maher that I found who was born in 1934 in Massachusetts was listed as Joseph M. Maher. He was enumerated with his mother, Helen (age 32, divorced, finished high school, waitress at a restaurant) and her brother, Leo Cloutier, age 42, divorced, a baker. Helen and Leo were both born in Boston.
It's unlikely that this is your Joseph. Without a little more information, we may not be able to find him in the index.