Cut the hole into a clean square or rectangle
Measure the opening
Cut a drywall patch to fit the opening
Cut two wooden backing strips longer than the hole
Insert the backing strips behind the drywall
Secure the backing strips with drywall screws through the existing wall
Place the patch into the opening
Screw the patch into the backing strips
Apply drywall tape over all seams
Cover the seams with joint compound
Let the compound dry
Sand the surface smooth
Apply a second coat of joint compound if needed
Sand again after drying
Prime the patched area
Paint to match the wall