Hi jomalomo and welcome, You just carry on as you are doing asking questions and I bet your nan will be more than happy to reminisce, most "mature" folks are glad of an audience.
While you are listening, and great idea of Wendi's to take a recorder, don't forget to try to pinpoint which sides of the family people are, she may well talk of relatives of her husband, her father or her mother and afterwards you might well wonder who they are connected to. A good idea also is to try to pin her down with dates, perhaps not definite years, but maybe something that happened about the time of, say ... the Great War, or another event which would help identify a birth, death, marriage or anything else.
Good luck and I'm sure you'll have lots of fun.
Mary