The new panel arrived, and it looked good, so I got to work. First I removed the old panel by cutting out most of it with a jigsaw, and drilling out all the spot welds (90 or so) that held in place, using a special spot-weld-cutting drill bit. Then I had to clean up all the edges of the surrounding metal where the spot welds had been, including grinding off the remaining parts of the spot welds.
I also had to fabricate and install a patch for a damaged section of the trunk floor, where many years ago a muffler mounting bracket had been torn off and crudely repaired. Finally, before welding in the new panel, I had to completely remove all the undercoating and paint from both sides of the metal where the new welds would be, on the edges of both the new panel and the mating surfaces on the car body. Once all the preparations were finished, I fitted the new panel into position, and used an electric spot welder to weld it in place. The actual welding went pretty quickly- 90% of the work was in the preparation.
I still need to spend a bit of time tidying up the welded joints, and installing new capping strips over the joints behind the rear wheels. Once that is done, I can get back to the actual paint job I had originally set out to do.