Jump out of either the submarine or Zodiak Boat (Dinghy) into water toautomatically be wearing the scuba gear. Note that you can't carry scuba gear as an item. Go to these locations to find the submarine and Zodiak Boat (Dinghy):
Submarine When you buy the "Sonar Collections Dock" property there will be a submarine that spawns at that dock. Also, after completing "The Merryweather Heist" (Offshore Option) mission, a submarine will start spawning at Sandy Shores Airfield. Pick it up using a Cargobob air transport plane (press Right on the D-pad), and then drop it in the ocean where you want to use it.
Zodiak Boat (Dinghy) At the west side of Elysian Island is a Dinghy at the Port of Los Santos. You can find another one by going to Miriam Turner Overpass, and searching next to the barge. There is also one on the southwest side of the Post Op depository.