Buying my rented house

I have been saving for a mortgage for years and now finally have enough for a deposit. I've been looking at houses in my local area and have realised that I love my house I currently live in. It's rented so how do I go about asking my landlord if there is any chance she will sell to me? Do I offer more than it's worth? If any body can give me their experience on the subject I would be greatful