How do I make a mattress cover?

I want to make a mattress cover like the ones that my grandmother used to hand quilt for babies. I have no idea how to proceed. I need something like that for a single bed and it must cover the entire mattress. My sister (74 years old) has cancer, she has lost a lot of weight and now finds her mattress very uncomfortable. We want her to buy a new mattress but she does not want to do that. So I am thinking that if I could make her a think mattress cover something like I describe above that it would make her bed more comfortable. Over this hand made pad, I would get her one of those foam covers to make it even more cozy. Does anyone know how I should proceed with this project. Many thanks.