Very carefully. Seriously, there are cable tv shows showing the flood-able “stage” that the put along side the fishing boat. They hook a shark and work it over to the stage side of the boat, then raise the stage out of the water. They shove a water hose inside the shark’s mouth to keep water flowing over the gills while the researchers apply the tags & remove the hook.
I used to love watching that show about tagging the sharks. On NatGeo?
Actor Paul Walker spent a season or two tagging sharks. He seemed pretty knowledgeable.