Remove the old keyboard by heating the "rivets" with hot air set at approx 200C. Use small nozzle and start from one corner. Pull the keyboard and heat the rivet, it will let go when hot enough. Go slowly rivet by rivet until keyboard and eventual reinforcement sheet is removed.
After that you need to clean melted remains of what is left of rivets, so that you can install new keyboard over them. I just use small bent tweezers and pull the remains.
Install the new keyboard and reinforcement metal sheet if there is one and double check that everything is on its place. New keyboard must lay perfectly and you must check every rivet (hole)! There is no going back if you find the error during next step!
Old cleaned rivets are barely long enough to be used again, but so far I never had a problem with them. You need to melt them again with the soldering iron. Set temperature at 230C or so and use conical or flat tip depending of rivets size and geometry. I usually use flat tip. Just squeeze the keyboard right next to the rivet and swipe the soldering iron tip over the rivet. It usually takes me half of second per rivet. Don't hold it longer and don't overheat, you'll just make a mess.
I have replaced maybe 10 keyboard using this method with 100% success.