Adoption!!!! Biological grandparents etc...?

As a child my mother was adopted. She has had a good life. My grandmother died 2 years ago and my mum has started to question whether or not she would like to find out where she came from. She has always told me and my brother, if we wanted to find out where she came from (our biological grandparents) we could. We had our doubts. Recently my mum and I have been talking about it and we would like to find out more, although my mum does not want to do it personally, she wants me to do it. Can I get the information we need as a biologoical granddaughter...???? and where do i start as my mum knows nothing about her birth name, where she was born etc etc..