Put at least a couple layers of masking tape on card under heatsink edge(s) to protect PCB. If you cover surface-mount parts like chip caps or resistors, mark where they are so you don't accidentally crush them later.
If the heatsink is held on with epoxy (no clips, heatsink does not move AT ALL at the base) then put it in a bag and in the freezer to make the epoxy brittle.
If heatsink has clips and/or it (ever barely) wiggles back and forth, it most likely uses either very thick paste or phase-change pad and should be put into the system and ran to be heated up, then worked on while still hot. Wrapping masking tape around heatsink itself would make it even hotter but might be overkill.
Either way, you'd then twist the 'sink or pry up from bottom with screwdriver blade (on masking tape to protect card), whichever seems most appropriate. Naturally if there are clips those would be removed first.