The Lurelin Village Chief, Rozel, is standing out on the dock during the day. Speak with him and ask about "the ocean" to learn about sunken treasure and get this sidequest.
Note: Rozel also has plenty of information about the surrounding area, such as the mysterious Eventide Island and some nearby ruins, so feel free to ask him about whatever you want.
Travel far out south where the water becomes an open ocean. You can either use Rozel's raft with a Korok Leaf or you can do it the slow way and use Cryonis to get all the way out there.
You will see three sharp, pointy rocks that form a triangle. There are some Octoroks and Lizalfos hanging out in the water so beware. Go to where the center of the triangle is and use Magnesis. You will see four treasure chests.
Once you have pulled up and opened one, your quest objective will change, so you technically don't need to open all of the chests to complete this sidequest. But why would you just leave behind unopened treasure chests now that you're here? Open them all for a Topaz, another Topaz, a Sapphire, and a Thunderblade.
Once you have spoken with Rozel again, the sidequest will conclude.
Note: Don't write off the ocean as another boring place! In addition to several unique species of fish, there are plenty of other places treasure chests lay in wait for you. Always scout out a body of water with Magnesis before passing it over.