Dissolve sea salt in water to make brine. Drop garlic into bottom of a wide-mouth, quart-size jar. Fill the jar with sliced radishes to within 1-2" from the top.
Pour brine over the radishes to cover, leaving about one inch of headspace. Place a glass weight on top of the vegetables to make sure they remain submerged.
Cap jars with an air-lock if you have one, or screw a lid on loosely. If you use a regular lid, be sure to loosen it daily to allow built up gasses to escape.
Set aside at room temperature for a week or so. The radishes will bubble and begin to take on a tangy odor. Allow them to continue fermenting until the flavor is to your liking.
Once fermented, store in the refrigerator indefinitely.
Notes
Water: Municipal tap water contains chlorine, which can inhibit fermentation. Be sure to use filtered or distilled water instead.
Salt: Salt with iodine or anti-caking agents can inhibit fermentation.