How to catch sharks
First of all, some general advice before going into the details of certain breeds. All of the sharks in Animal Crossing: New Horizons spawn in the ocean, often near the pier although this is not required, and feature a unique shadow that you won't see for other fish. Instead of just the shadow itself, you'll also see the dorsal fin sticking out.
When you see this you know you have a shark ready to go. The rest is pretty much the same, just throw your line in front of them to get their attention, then wait for them to bite and pull the bobber underwater. The reward will be the Ten Thousand Bell Fallen, or a sophisticated addition to your museum.
There are four sharks available in the game: the whale shark, hammerhead shark, saw shark, and great white shark. All of them are rated differently but will appear around the same time. Shark season runs from December to March in the southern hemisphere and June to September in the northern hemisphere. While the great white shark can spawn at any time of the day, the other three will only appear between 16 and 9 a.m., so try to stick to night fishing if you want one.
There is a way to get a lot of sharks, but unfortunately it's pretty hit and miss. Shark Island is over there, and is just a Nook Miles ticket. However, there is no way to guarantee that you end up there when you make the trip. If you do, be sure to fill your inventory with it. And for more tips on catching sharks and other rare fish, check out this guide.
In terms of selling price, hammerhead sharks are the cheapest at 8000 bells, saw sharks are at 12, whale sharks go at 000 and great white sharks have struck 13 bells tying the coelacanth for the highest grossing fish in the game. So I hope this helped explain how to catch sharks in Animal Crossing: New Horizons, because you'll want a lot of them.