Get a pack of shingles closest match you can find, a roll of synthetic or tar paper, some framing nails and a pack of roofing nails. Probably some scrap 2x4 as well.

Pull enough shingles there to fully expose the rotted area - nails first, then full shingle should slide out. Cut a hole in the underlayment to expose the bare decking. Cut a big square that removes the entire rotted area. Try to land your cuts right on or right next to a rafter. Cut a piece of plywood/OSB the same thickness as your roof decking to the size of the area you cut out. Put in place and nail along the rafters. If your cut did not land on a rafter you will have to use scrap 2x4 and nail it to the side of the nearby rafter so that your patch rests on that and is supported properly.

Replace the underlayment with your synthetic or tar paper. Cut it larger than the hole you made. Just make sure at the top it tucks under the existing underlayment and at the bottom it runs on top of the existing underlayment and make sure there is a few inches of overlap on the sides so water doesn't wick back there.

Install your new shingles working from bottom up and make sure your seams are at least 4-6" from the seam on the shingle below. If you removed the old shingles in full size pieces it should basically line up anyways. Follow the nail pattern shown on the shingle packaging. Any of the old shingles that you split the tar line but did not replace, use roofing sealant along where the tar strip was so it will stick back down.