This is an old project from 2000, so please excuse the low res pictures. This is a hydro setup similar to my recirculating hydroponics with the exception that it uses an air pump instead of a water pump.
Step 1: Parts
a pair of buckets, check you local grocer's bakery, they'll often have them for free or a buck.
an air pump
a piece of pex tube 3/8ths
1/4 inch irrigation connector
barbed hose elbow
Step 2: The Bottom Bucket
drill a 3/4 inch hole near the bottom of the bucket, insert the grommet and barbed hose connector, attach the clear tubing. This serves both as a water level and as a drain, you can do with out, but draining will require disassembly.
Take the lid and drill several 3/4 inch holes in it, Snap onto the lower bucket and drill a 1/4 inch vent hole in the side of the bucket near the top.
Step 3: The Air Lift
Using a piece of 3/8ths PEX tubing cut one end at a 45 degree angle, drill a hole in the side of the tubing about 1.5 inches from the bottom and insert the 1/4 inch irrigation connector, attach the aquarium tubing to the connector.
Insert the air lift into the bottom bucket.
Step 4: The Top Bucket
Drill some holes in the bucket bottom, slide over the airlift and slip a piece of window screening into the bucket.
Step 5: Finally
Fill the top bucket with perlite, fill the system with nutrient solution by pouring in through the top bucket, attach an aquarium pump, clip the pex airlift so it extends about an inch above the perlite and invert a film canister over the pex. Now you're ready to plant.