Having watched my builder's fix-it guys doing work on my house, I can attest that the method in this article is what the pros do and it works well.
I've had good luck with the plastic mesh for a decent sized hole, it takes several passes of covering it liberally with compound and sanding to get it, and the texture is going to be too smooth, but from a distance nobody'll see it.
For box holes that are too big, where too big is 1/4" to 1/2", I've been able to build out from the drywall with blobs of compound, adding some each time. The key here is that the compound sticks to itself or the front face of drywall pretty well, but not to the gypsum edge. So you have to at the least reach beyond the extension of compound and hold it in place and be very gentle, or you'll "break" it right off the edge of the drywall. Again, the end result will be too smooth, but from a distance nobody'll see it. I did a lot of wall box cut-outs this way, and it worked okay. A few had to be done a few times due to this breakage issue... you're almost there, doing a final sanding pass, and it just crumbles away...