Place the bucket in an area of your home or garden that receives good natural light.
Drill several holes along one side of the garden hose. Coil it around the inside of the bucket, orienting the hose so that the holes are facing into the center of the bucket.
Place the aquarium pump into the bottom of the bucket and attach it to the garden hose. Close the other end of the hose with the rubber stopper.
Mix a nutrient-rich solution. Mix the hydroponic nutrient solution according to the instructions on your brand's label. Use only bottled mineral water or filtered water. The kind of solution you will need will depend on the plants that you are growing and the growth stage they are in.
Place a nutrient-rich solution into the bottom of the bucket. The aquarium pump will pump the solution through the hose, which will spray it over the plant roots, and the solution will return to the bottom of the bucket.
Use the craft knife to cut a hole in the bucket lid just large enough for the 3- to 4-inch pot to fit in snugly. Place the pot into the lid and fill it with clay pellets.
Plant your seedling in the clay pellets. Hand water the seedling until the roots begin to hang down between the clay pellets. At this point, you can begin misting them with your home aeroponics system.
Check the pH of your nutrient-rich solution regularly with the pH testing kit. The nutrient-rich water may become unhealthy for the plant over an extended period. Ensure that the solution has a pH of between 5.5 and 6.5. Try to keep the pH as close to 5.5 as possible.
Change the nutrient-rich solution every two weeks. This will ensure that you replenish the nutrients your plants have consumed and avoid a nutrient imbalance. Run the system with plain water for one day every four weeks to flush out any nutrient buildup.