There are mainly five types of hydroponics system

• Wick System
• Nutrient Film Technique
• Ebb and Flow
• Deep Water Culture
• Drip Systems

Wick System
The wick system involves providing nutrient to roots via wicks from a tank which stores nutrient solution. This is most basic as it generally does not involve any moving equipment. The material  of wick can be anything which is porous and can absorb water such as ropes, Felts etc. The size and  number of wicks should sufficient to supply nutrient more or equal that water plant can absorb. Due to this limitation it is good for small plants.
Nutrient Film Technique
Nutrient Film technique or popularly known as NFT. The plants are grown in channel or Pipe with nutrient solution running in the pipes in a thin streams. care should be taken that roots should not dry and sufficient nutrients are available in all the plants. Plants are planted in netpots having suitable dimension depending upon plants and separated at a distance. The separation and  size of netpots will depend upon plants species. This also requires a pump for nutrient circulation and air stone for providing aeration to nutrient solution. The pH and temperature of water is important.
Ebb and Flow
In Ebb and flow, the plant is grown in a tray filled with a growing medium. The tray is "flooded" with your nutrient solution a few times per day, depending on factors like:

• The size of your plants
• The water requirement of your plants
• The air temperature
• Where your plants are in their growth cycle etc.

Flooding is accomplished by using a reservoir below the tray, a water pump, and a timer to schedule the flooding cycle. After the tray is flooded, gravity drains the solution back down into the reservoir, where it is being aerated by an air pump and air stone. It sits there waiting for the next flood cycle, and the process goes on. Hydroponic growers choose ebb and flow systems for their flexibility. Most of them will fill the tray with a growing medium of their choice and also add net pots to organize their plants and control the roots a bit more.​
Deep Water Culture
In a Deep Water Culture  system, a reservoir is used to hold a nutrient solution. The roots of  the plants are suspended in that solution so they get a constant supply of water, oxygen, and nutrients. To aerate the Nutrient Solution, an air pump with an air stone is used to pump bubbles into the nutrient solution. This prevents your roots from drowning in the water — a weird thing to think about, but it does happen to many beginner hydroponic gardeners. Your plants are typically housed in net pots that are placed in a foam board or into the top of the container that you're using for your reservoir. With some hydroponic growing media added into your net pots, they provide a home for the very beginning of your root system and plant stems.​
Drip System
In Drips system the nutrient is pumped through a drip system and stored in reservoir. It is very simple to use and quite popular in commercial system.
You can buy hydroponic nutrients at https://tripathiproducts.in