For the structure of my hearth, I chose what is becoming a more common material: metal studs. They're easy to work with, provide a non-combustible base and backbone for the hearth, and are pretty cheap.
To hold the studs to the walls, I located as many of the metal studs over the actual studs inside the walls. You can use a stud finder to find the studs on your walls if you need to. Unless you're sizing your hearth based on the studs in your walls, though, you won't be able to screw all of your metal studs directly to the studs inside your walls.
But that's okay, because 3M makes Command strips. Ha ha ha ha.
