Have your grandparents passed away?
If so start by getting a copy of their death cert's. That will give you at least some data (although it is secondary) to go on. At the very least, you'll have their birth dates and locations,.
Next, their marriage record is the next document to obtain. You don't know what you'll find on it, until you see it.
Their social security applications are also another set of docs you'll want.
Oral history is good for leads, but the paper is evidence, and that's what you need to obtain.