First, you need to get rid of calcium deposits inside the air stone. Soak it in warm vinegar for several hours, then rinse out with water. Next, you need to heat up and break down things that won't dissolve in the vinegar bath, so you put the stone into a pot of boiling water for another several hours. The final stage is using a base corrosive to take care of anything else left over - soak in water with chlorine bleach, 3:1 water:bleach, for 24 hours. Remove stone from the bleach solution and rinse thoroughly with lukewarm water for about ten minutes, until it no longer feels slimy. If you can force water through the air stone, do it, otherwise just keep rinsing the crap out of it.
Allow to dry and store, or after rinsing immediately put back into your hydroponics system and get that airflow going! You won't have 100% airflow restored but you will have a great deal returned to you!