Paint an underwater scene on a canvas backdrop. Start with a blue background and then add in color and detail by painting a large coral reef, some tropical fish, seaweed, perhaps a shipwreck, and maybe even a scuba diver or two in the background. For a less realistic scene, you might include mermaids or an underwater city.
Dump bags of sand around the stage. Keep sand clear of heavy trafficked areas; no actor wants to slip and fall in the middle of a sold-out show.
Place large rocks, seaweed, coral, and seashells around the stage. Papier-maché boulders are often used in outdoor scenes, and these will be ideal for your underwater set. Make sure that the seaweed, coral, and seashells are also kept out of high traffic areas.
For a less realistic play, you might place a wooden chest on the stage, fill it with old newspaper and cover the paper with faux gold and jewels, creating the illusion of a treasure chest brimming with goods.
Replace some of the lighting with blue light bulbs. This will set an underwater atmosphere. Be sure not to replace all the lights: you want the audience to notice the details that are in the set and if it is too dark they won't be able to.