How to swim
You need two important things to dive. The first is the current summer update for Animal Crossing: New Horizons, which arrives Friday, July 3. Although the southern hemisphere is currently in winter, the update is still the same, as is the process that you have probably gone through a few times before. For those who haven't, starting the game should trigger it, but to force an update you can tap More on the game icon to find the update option.
Once downloaded, a key piece of gear will be added to both Nook's Cranny and Nook Stop in Resident Services. Wetsuits are a requirement for swimming and snorkeling in the game, but you can purchase them directly from Nook's Cranny for 3000 or at Nook Stop for a currently undisclosed amount of Nook Miles. Once you have it, you just need to put it on and then head to the beach for a swim in the ocean.
In the trailer, it looks like you can just get started, but don't be surprised if you have to press A or Y to do so. Once in the water, you can swim as if you were walking, but you'll want to get under the water to catch these important creatures.
How to dive
Whenever you swim around the ocean in Animal Crossing: New Horizons, you can dive underwater to see if there are any precious or rare creatures / items to grab. If it follows how it worked in New Leaf, all you have to do is hit Y and you'll go right below, although they can pass it to A, so wait for an update once. the official patch released. Once under the water it looks like you can swim a bit. If you see a shadow, similar to the shadows of fish near the shore, you can swim up to it and grab it to bring it to the surface and put it in your pocket.
After that, you can return to earth to donate them to the museum or sell them for Bells. But don't rush as there are visitors like Pascal to interact with, so be sure to explore. Otherwise, that's what we currently know about how to swim and dive in Animal Crossing: New Horizons. Check back after the update is complete for more details.