The Animal Crossing: New Horizons Summer update has added a whole new type of creature to track down and add to your collection. You can now swim and dive, and find sea creatures to bring to Blathers or sell in the Nook Shop. Needless to say, all of them can be caught in the sea, but you will need to get yourself a swimsuit to be able to go after them. If you head to the Nook shop, you will be able to grab one from the Terminal for 3000 Bells.
The Spider Crab can be found at any time of the day, between March and April in the northern hemisphere, and between December and March in the southern hemisphere. To catch them, you will need to go swimming and then dive down where you will be able to see some shadows.
With your swimsuit equipped, face the sea and press A to jump into the water. Swim around and look for bubbles coming to the surface. Press the Y button to dive under the waves, and aim for shadows that were producing the bubbles. Grab the shadows to come back up with some form of sea creature, and hopefully one of them will be the Spider Crab. There are 40 new sea creatures in the game, so it might take you a while to track down the Spider Crab.