There's an airstone, clear air line tubing, and air pump required. A check valve in the line may be required if your air pump is mounted below the water level.
All can be obtained at Petco
or the fish department at a local pet store. Here's a selection of air pumps
at various prices and outputs, at Walmart, and they should have the lines and air stones/bubblers as well.
And I didn't mean to imply that you should buy an Aerogarden, only that that's what I'm using now. It was a gift from Floger. He wasn't using it.
Hope this helps, 52.