An update to Animal Crossing: New Horizons in summer 2020 allowed players to leave the shore and swim around their island. After being given a wetsuit, you can swim around and find all sorts of sea creatures that you can't find by fishing.
Animal Crossing New Horizons how to swim
Go to Nook's Cranny on your island and go to the cabinet on the right. Open it and you will see a number of different items that you can buy on site. One item is a wetsuit with horizontal stripes that sells for 3,000 Bells.
If that particular wetsuit doesn’t suit your fashion sense, you can also purchase a turquoise and black wetsuit with your Nook Miles. Go to the terminal in Resident Services. You can find the Nook Inc. wetsuit for 800 Nook Miles. You can also purchase a Nook Inc. snorkel for 500 Bells, although this is not required for swimming.
Make sure you have a wetsuit in your pockets. Open your pocket inventory and equip/unequip the wetsuit. It will go over all your other clothing, which goes back into your pocket inventory. This won't take off your shoes though – it shouldn't affect your swimming, but you might look ridiculous splashing around in the water with a pair of boots on.