Patching a large hole in drywall is part having the right products to work with, part having the right tools and part technique.
Rule one is that hard plasters, like Polyfiller and Durabond 90 and others, are good to use to fill large cracks, but should never be brought right up to the finished surface because they are so difficult to sand. Once the patch is in place and the worst is filled in with either setting plasters or a piece of drywall, the rest of the work is done with joint compound because it is the best for a smooth sanded finish.
Always tape joints, or they will crack later. One important detail is to trim off all edges that want to come forward into the joint compound, as you see in the photo..
Always let joint compound dry completely before continuing, or it will shrink more than you expect. It may be dry on the surface, but if it is cooler than the drywall around it, it is still evaporating off water. Wait until the temperature of the patch is the same as the wall next to it before moving on to the next coat.
The final finish on a patch may reach as much as two feet away from the original hole. The inexpensive trowel to do this is simply a straight piece of 1x3 wood with a slightly rounded and well sanded edge, as you can see in the second photo. A coat of hard car wax on the 1x3 will keep compound from sticking.