First of all you should know what you want to grow and why. Choose something which you really need. For instance, if climate of your area is not suitable for vegetables then grow them in your hydroponic garden.
If you are doing for the first time then you should grow plants in limited numbers. However, you can grow different type of plants as it will really help you understand the needs of different plants.
You will have to check as to how much space you will need for your small hydroponic garden. Normally, a setup of six square meters is enough to grow 66 plants of cabbage or silver beet. Keep in mind that these plants require more space than any other vegetable plant so numbers vary with nature of plants.
Prepare plastic buckets and tubs by drilling holes in their sides. Make sure these holes are one inch above from the bottom. You will need this equipment to store nutrient solution, the liquid in which you are going to grow your plants.
Now it is time to prepare the nutrient solution. You can get this easily from market but if you are making your own then be careful while mixing ingredients. Measurements should be correct otherwise it will not yield favourable results.
Fill your buckets with solution and then place them higher than the tub. Let the solution flow into the growing medium and saturate it.
Now you will prepare seeds to plant. Wash them gently to remove the dirt from their roots. Read instruction on the packet and then start planting them.
Place your seeds in the growing medium at equal distance and arrange some fresh air which will help them to grow fast.
Keep checking the chemical balance every day. You will have to maintain water level properly.
It will take the plants three to four months to grow. Be patient and harvest when it is needed.