A desoldering tool, aka solder sucker, and a roll of rosin core solder.
There are several tricks, like replacing a multi-pin IC, you can clip the leads away from the body of the IC and then remove each pin one at a time. To clip those away, I use a pair of flush cut nippers with somewhat long thins tips. And you slap any hands that try to grab those and cut bolts.
If you need to use the solder sucker, sometimes there isn't enough solder on the component to efficiently suck away. In that case I add some solder before I try to remove it all.
If I wish to remove a complex IC and I don't want to or can't cut the pins, I carefully mask off that IC (both sides) from the rest of the board (really well) and use compressed air (safety glasses of course). A quick blast of air aimed at molten solder will blow it away and any that is left will be a cold solder connection. Note, that molten solder will go everywhere so the masking must be perfect and all precautions observed.
There is a long list of how-to that comes from experience.