There are multiple types of Hydroponics systems. Deep Culture/Floating Raft Systems take up a lot of space 
but have a very high yield. Stacked grow beds are very efficient by utilizing vertical farming and hydroponics systems while also providing high yields. Potted or container, also known as Dutch Bucket system, works well with Hydroponics systems. Also a large bed with clay balls works well for melons, squash, etc. See below for many examples of the different types of systems. Media based, NFT and Deep water culture are just three of the types - see the link below for a brief introduction on these 3 types. See above for the diagrams of the most common types. See below for more detailed information on each of the different types. Click on the video link below to see a short video detailing how to set up a very basic hydroponic system (good project for kids).
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Click Here: Beginner Hydroponic System Project
Nutrient Film Technique (NFT) Systems
One system that has proved to be very productive and combines aspects of the vertical gardening technique is the NFT system. With this system, you can utilize many different configurations in order to utilize your growing space. The NFT systems can be built out of gutter or PVC pipe. See below for multiple ideas for NFT configurations from multiple building materials.
Click here: Multiple NFT System Designs
Hydroponics Raft (Deep Water Culture) System
Floating beds are grow beds with flotation with holes drilled in it. The holes contain baskets with a grow media and a plant. This allows the roots of the plant to be immersed in the water all the time. Floating beds are best for cruciferous plants such as spinach, lettuce, kale, chard, mustard, collards, basil, mint and most herbs. Raft systems can be the cheapest systems to build but take up a lot of space.
Read more: Raft system information
Vertical Hydroponics Growing Systems
Vertical systems are designed to fully optimize growing space. The structure of your vertical system can be 3 feet tall or 30 feet tall depending on your facilities and the strength of your water pumps. There are many different types of vertical systems. Some can be built for less than $100 or some can cost $1000's. This resource can give you all the information you need to determine the type of system you want and to help you design and build the system that works for you.
Hydroponic Dutch Bucket Container Plant Systems
Hydroponic systems can be set up for Container plants ensuring better growth and production than regular watering. Utilizing different types of growing medium will ensure that your plants retain moisture and retreive needed nutrients for optimal growth and production. .