It depends on the instructor. I took this class, and was very pleased with it. The instructor is the owner of the LDS, an avid freediver and tournment spearfisher. He also runs spearfishing only charters and writes occasional pieces for the local newspaper (spearfishing reports).
As for the class, as usual, safety was of prime importance. Then a background of the various types of spearguns (e.g. Sling, pnumatic, banded). And the advantages/disadvantages of each type and of the possible materials it can be made from. After a heavy emphasis on safety, on to local federal and state regulations regarding spearfishing. Proper ethics for spearfishing, including only catching what you are going to eat, and never more than needed. How to properly identify the size and species of fish. Where to target each different species, and it's habits (e.g. if shot will it run, try to hide in a hole/under a ledge, will it come back at you?). How to remove the fish from the spear and put it on the stringer, where to keep the stringer, what to do if a very large predator wants the stringer (give it to them, if it's not a species you want). Getting in/out of a boat with a speargun. After all this and more, time underwater, proper loading/unloading techniques, how to aim / shoot.
Overall very pleased I took the course, cost was $70, class consisted of 2 days, 3 hours each.