When you’re just learning to sketch, you use graphite. Why? It’s cheap, great at training you to recognize different shades, and most of all, it’s erasable. When you’re learning, you’re going to make mistakes, and un-making them is an important part of the game. Same goes for electronics, of course, so when you’re teaching someone to solder, don’t neglect teaching them to desolder
We could argue all day about the best ways of pressing the molten-metal undo button, but the truth is that it’s horses for courses. I’ve had really good luck with solder braid and maybe a little heat gun to pull up reluctant SOIC surface-mount chips, but nothing beats a solder sucker for clearing out a few through-holes. (I haven’t tried the questionable, but time-tested practice of blasting the joint with compressed air.)
For bulk part removal, all you really have to do is heat the board up, and there’s plenty of ways to do that, ranging from fancy to foolish. Low-temperature alloys help out in really tough cases. And for removing rows of pinheaders, it can help to add more solder along the row until it’s one molten blob, and then tap the PCB and watch the part — and hot liquid metal! — just drop out.