Pro-tip: If you get a board with the caps with the little legs on the side, use a ring type puller and don't pull straight up, but slightly to the side. You won't ever have an issue with the switch top coming off with the cap.
The way I pull these is with a butter knife or similar sturdy flat piece of metal. You want to pry upward from under one side (side, not front/back) of the keycap while pushing sideways from the other side of the switch. In other words, push the keycap in the direction of the side that you’re prying up from the bottom. One of the little clips that hold the keycap down will snap free (the one on the side you’re prying), and then you can pretty easily push the keycap back the other way to disengage the other clip.
This is probably easier to demonstrate than to explain in words. :-)
I’ve found the most efficient way to remove a bunch of caps is to do them in batches: first unclip one side of the keycap for (e.g.) every other keycap, then come back and lift those all off, then unclip the rest, then lift those off. It’s actually pretty fast once you get a system going.
Of course, the easiest is if you have the old “Gundam” style of switches; then the caps don’t have the little clips at all and you can just lift them straight off.