We are called on most every day to provide drywall repair - so we have gotten pretty good at it!
This sample is a bit toward the extreme of what we find, however it illustrates how we go about creating a lasting and compatible solution.
First, the hole must be stabilized and supported. For small holes, it can be a simple patch. For larger damage, we have to construct a framework for the new drywall piece to adhere to.
Next, the seams are filled with drywall mud and covered with drywall tape or vinyl mesh. Then this is covered with the first of three layers of drywall mud.
To create a seamless repair, you usually need three layers of mud. We use the "full strength" drywall compound which requires a full day to cure and dry. Some of our competitors use the 20 minutes or 45 minute stuff. We are frequently called out to correct their brittle, weak repairs.
Finally, a good sanding to feather the edges into the existing wall and two to three coats of paint; to a) seal the new drywall and the mud, and b) blend with the existing wall (or ceiling). And you have a professional repair.