You just measure around the circumference of the quilt and divide that by the width of the fabric you are using, then multiply by the width of the binding strip you are using (usually 2.25 or 2.5 inches). That gives you the number of inches of fabric you need to buy for the binding.
For the backing, you determine the width of your top. If it's more than 40 inches wide, then you will need more than one length of fabric. You would then determine whether you want to buy 2 lengths of fabric or piece the backing. Piecing the back is done many different ways. Some people use leftover blocks to add to the width or length of the backing. There is a method to use a diagonal seam on the backing (google it). There is no cut and dried way to do a backing. I once had to go back for more backing for a quilt. By then, they had a new die lot and it didn't match. I made a piano key border that I used between the two different pieces of backing fabric. By the time that was in there, you couldn't tell they were two shades of red.
As others have said, it's easier to figure after you have the top done, but you can guesstimate pretty close if you have an idea what size your quilt will be.
bkay