When you enter the water on the beach, your persona will start swimming.
To just continue swimming in a specific direction, you can use the general movement keys (W,A,S,D, or Up, Down, Left, Right), or by holding down the Left and Right Mouse Buttons at the same time.
CTRL will make the character dive under water. Releasing CTRL will release the dive.
To swim back up, press SPACE. If you are at the surface and press SPACE, your persona will jump slightly out of the water.
You can swim faster by holding down SHIFT