The blue waters around the Corn Islands are not only perfect for swimming and diving, but they also offer great sport fishing opportunities. From both Big and Little Corn Island you can hire a boat and go out fishing.
The easiest way is finding somebody who can provide a rod and other fishing equipment (which is not hard as there are several shops and fishermen who offer this service), and then let somebody take you to the fishing grounds.
The most often caught fish is barracuda. Rods are equipped with fake bait and the boat will slowly make its way through the water while the bait trails behind it. You just manage the rod and wait for the fish to bite. Simple but effective. Almost never does a boat come back empty-handed. Besides the barracuda you can catch red snapper, bone fish, or even sharks. Sharks are protected and should be released. The other fish can be brought home to be used in the evening's dinner!
You can rent boats and equipment for around $20 an hour for two people. Ask your hotel who can certainly point you to somebody who offers this service.