From a lot of trial and error adventures I found the following to work.
Cut a patching piece of drywall roughly square, somewhat larger than the hole you are trying to repair. Then, holding the patch so it covers the hole, draw a pencil line around the patch then cut along the pencil line to make the hole match the patch.
Take a relatively thin but wide piece of wood that is at least a couple of inches longer than the longest dimension of the hole.
Have a drill with a phillips bit in it ready along with four drywall screws.
Snake the piece of wood inside the hole and hold it so that it diagonally crosses the hole and put a drywall screw though the wall and into the wood, snugging the wood up against the backside of the wall. Rotate the wood piece so that as much of the wood shows through the hole as possible and use another screw through the wall and into the other end of the wood.
Now the wood will support the patch in the next step.
Mark the wall with pencil marks so you know where the wood disappears behind the wall on both ends of the hole.
Prestart the two remaining screws into the patch before putting it into the hole and back out the screws so that the points of the screws don't protrude out the back side of the patch.
Now, gently fit the patch into the hole and without applying much pressure on the screws, slowly run them into the wood through the patch until the screws are just snug and slightly dimple the surface of the patch.
The patch will now not shift, the main reason for cracks in taping. Prefill the crack around the patch with a very thin coat of spackling. Let dry a couple of minutes then repeat, gently pressing the spackling into the crack. Now use either paper tape (if the crack around your patch is like a hairline, or mesh-type tape if the crack is larger then say havel the thickness of a pencil.
Multiple very very thin coats which go on a fast, dry quickly and require almost not sanding... this will make the job easy and look nice when you are finished.