You can buy stone veneer that looks just like the real thing. We have a fieldstone fireplace in which stone veneer goes from the floor to the ceiling. We had ours professionally done but I know they built the wall out a few inches with lumber so that the stone looked like it has a lot of depth.
The veneer comes in small sections that you just apply with mortar. I have done a brick wall myself
I imagine that working with stone is a similar process.