Tape the Joints and Apply Compound
Cut pieces of mesh drywall tape to cover the edges of the patch, and press them into place.
Using a 6" or 8" drywall knife, spread joint compound over the tape, just thick enough to cover the tape. Do not wrinkle the tape.
Allow the patch to dry for 24 hours, then apply a second coat, feathering the edges.
Once the patch has dried, smooth it with fine-grit sandpaper on a sanding block, feathering the edges.
It may take 3 or 4 coats to get a perfectly smooth patch.