Once the fish is cool, pick the meat from the bones. This is best done by picking towards the back of the fillet. The bones tend to face toward the fish's tail, so if you pick with the grain, you can lift out big chunks of boneless meat.
A word about the centerline. The centerline of a bony fish is often loaded with lots of teeny bones, sticking right into the fishiest-tasting part of the fillet. My advice is to toss this section.

