You have the right idea.
To start, if the existing hole is framed all around using 2x6 or whatever size studs you have, add framing so you have nailing for the exterior plywood and the interior drywall. If the opening is in between the studs, you will have to install backing plywood "splices" to give you something to attach to, and use screws on your drywall and plywood patches as well.
For a shingled wall, you have to remove some of the shingles around the opening so that you can install some tar paper or other waterproofing housewrap (best to use what is used elsewhere) and "shingle" the patch correctly. Meaning, the top of your patch should tuck under the existing, and overlap the wrap at the bottom, to shed any water that gets behind the shingles. Then reinstall the shingles. If your shingles are painted, pre-prime both sides and let dry, then install, then paint to match the color.
I use a 1/4" crown pneumatic staple gun for shingles, you may know someone with one you could borrow. If not then hand nail using small galvanized shingle nails, which are like very small box head nails, not finish nails, which can split the shingle.
Hope that helps.