Growing plants without soil is usually called hydroponic gardening. In hydroponic gardening, vegetable plants are grown in an artificial medium that draws a solution of water and nutrients into the plant's roots. Different nutrient solutions are made for different types of vegetables. Growing hydroponic vegetables allows you to control the nutrients received by the plants and can allow vegetable plants to produce larger harvests for a longer period than traditional gardening.
Select a container for the solution of water and nutrients. Containers can be anything from Styrofoam coolers, large plastic containers, or any plastic container between 2 and 3 feet high. The only requirement of the container is that it must have a lid you can easily cut holes in to insert mesh growing pots.
Arrange the mesh pots on the top of your nutrient container and mark the maximum lip of the mesh pot. Cut out holes slightly smaller than the lip of the mesh pot. Make the holes small enough to support the mesh pots.
Fill the mesh pots with a soil-free medium like perlite, vermiculite, or wool rock. This growing medium supports the roots and plants as they grow, but provides no nutrients.
Mix your nutrient solution with water in the nutrient container per manufacturer's instructions. Fill the nutrient container high enough that the solution covers the bottom inch or two of the mesh baskets when they are inserted in the container's lid. Reserve enough nutrient solution to thoroughly soak the growing medium after planting the seeds.
Put two to four seeds on top of the growing medium and completely soak the medium with the reserved nutrient solution.
Make sure the medium stays moist. If your mesh pots are submerged an inch or two in the container's nutrient solution, it should wick up adequately.
Maintain the levels of water and nutrient solution in the nutrient container. Make sure you have air space between the top of the container and the solution to allow adequate air space for the roots.
Select an out-of-the-way area and suspend a 4-foot, two-bulb cool white fluorescent fixture over the container. Mount the fixture on a chain. Constantly adjust the height of the fixture to keep it 3 to 4 inches above the top of the crop. Use a timer to keep the lights on 14 to 16 hours per day.
Keep the lights off until the seeds germinate. Turn the lights on for four hours per day once you see two leaves. Increase the amount of light the seedlings receive by an hour a day until you've built the plants up to between 14 and 16 hours per day.