Here's a system that is that can be built from materials you'll find at WalMart. This system will allow you to grow 6 plants at a time using the specified materials.
Materials
48 quart or larger plastic tub (about 15" by 20")
1 piece of 2-inch Styrofoam board, cut slightly smaller than the bottom dimension of the tub
6 large plastic cups (16-20 oz. disposable will work)
Perlite
Vermiculite
Small aquarium air pump
Length of airline tubing
Check valve (if your air pump will be below your garden)
Air stone (the long ones work better than the small round stones)
Water
Nutrient solution (available from hydroponic sources everywhere)
Instructions:
1. Drill about eight 1/4-inch holes in the bottoms of the cups. This will allow water into the cup and let the roots out into the water when they've exceeded the space in the cup.
2. Wash down the perlite and place in cups to a point about 1/2-inch below the cup rim.
3. Poke a hole in the middle the perlite in each cup (1-inch deep) and fill with vermiculite. The vermiculite holds moisture better for seed germination.
4. Place two lettuce seeds in the vermiculite and water gently until water runs out the bottom of the cup.
5. Cover the cups with plastic for a few days, until the seeds have germinated, making sure the vermiculite remains moist.
6. Cut 6 circular holes in the Styrofoam board (make sure the holes are at least 1-inch from the edge). The size should be such that the cups sit in the holes with the cup bottom being flush with the underside of the board. If the cup sits to high, the plants won't get water. If they sit to low, they might become waterlogged.
7. Place the cups in the 6 holes.
8. Connect the airline tubing to the air pump (and check valve, if applicable) and air stone. Place the stone in the bottom of the plastic tub.
9. Fill the tub to within 2 inches of the top with nutrient-enhanced water. Place the cup-filled Styrofoam board on the water. Place in a sunny location or under grow lights. (For the best results indoors, use two 4 foot fluorescent shop lights. Use two standard cool white tubes and two grow light tubes. Use of incandescent grow lights is not recommended. They put out too much heat.)
10. Turn on air pump and wait for the results.
11. Depending on the size of the plants and your container, the nutrient solution may need to be refreshed from time to time. Also check and adjust the pH for the particular crop you are growing. Thin seedlings to one plant per cup.
December Update:
You can use a ¾-inch piece of Styrofoam board (like found a building supply stores and lumber companies). It’s about $7.00 for a 4 foot by 8 foot sheet. Cut it slightly smaller than the bottom of your hydroponic tub and cut holes for your cups. You should use smaller cups, like plastic Dixie cups for bathrooms. You’ll need less perlite this way too.