How do I get items after they fall into the water?

Find something large and metallic, like a metal box or chest, and use that to push the thing you lost to the shore.

Cryonis will only create ice pillars starting just below the surface of the water, so it won't "push up" anything that sank.

You currently can't dive in Zelda. So if something falls into the water and you can't pick it up while swimming over it you are out of luck.

The only solution how you interact with items below the water surface is the magnesis tool. So you can try to drop a magnetic weapon (or search for something magnetic) and try to "fish" with it, to push it to the beach and pick it up from there.