So, according to the heading, this is your maternal grandmother we are talking about. You know, presumably (though we don't), her name, and where and when she died.
From her death cert, or from the entry in the gro indexes for her death, you will find her age at death if you don't already know it. That gives you an idea of when she was born.
From your mother's birth cert, you will find grandmothers maiden name. If you don't know your aunts and uncles names (if there were any children other than your mother) you can look for them.
You then know about when she was born, and what her name at that time was.
Hopefully you can find her marriage, now you know her maiden name, and the dates of when her children were born and what area.
Her marriage cert will then give you her fathers name.
When you get back to 1911and earlier, the censuses are there to help you see families together.
This is just basic Family History research. If you get stuck at any point, then people on here are happy to help you look, but will need to know names and dates that you have.
If your mother is still alive, then atart by asking her or seeing what documents she still holds.
