Not sure if there is really an easy method, but here is our situation with two pictures. It is a relatively large area (~1100 sq. ft.) inside a vinyl fence, so not easy to get heavy machinery in. I also built a box frame with hardware cloths like this setup, but an hour's back breaking work clears perhaps only 10 sq. ft. area since many of the rocks have sunken and mixed with the soil/dirt.
Sometimes you just have to bite the bullet. Everything is on the table. A fence is just a fence and can be removed and replaced, or not. Heavy concrete pavers can be removed and replaced, or not. With the pavers and the fence out of the way, a small digger/backhoe on tracks could take the stony soil out, be trucked away to someplace where fill for a foundation is needed, and replaced with good soil. Replace fence and other features as required. It is the long way around, but gets the job done.