There are several methods of hydroponic gardening.

Water Culture 

One of the simplest and most inexpensive systems is Water Culture. The plant is placed in a basket above a reservoir filled with nutrient solution. From there, the roots hang down, completely submerged in the solution.

Nutrient Film Technique (NFT)

The NFT system is a popular choice for home gardens. It involves a shallow stream of nutrient solution which flows through a downward sloped channel. This creates a thin film of nutrient along the bottom of the angled grow channel which can then be absorbed by the plant roots that hang into the channel.

Aeroponic

In Aeroponic systems the roots hang in midair within a growing chamber, without growing medium, so the entire root system can be exposed to oxygen. Within the growing chamber, the roots are sprayed at regular intervals with aeroponic misters.

Ebb and Flow 

The Ebb and Flow, or Flood and Drain, technique uses a water pump on a timer. It floods and then drains the root system with water and nutrients.

Drip System 

In a drip system, the plants’ roots are placed in a growing media such as perlite or gravel. Then, a water and nutrient solution is pumped from a reservoir, through tubes, to drip onto the roots.

Wicking System 

A wicking system is very simple. Plants sit within a wicking medium, such as vermiculite or perlite. They are in a container directly above the water and nutrient solution reservoir. A wicking rope or strips of felt are used to connect the wicking medium to the
solution.

The table that follows identifies the growing needs of the best vegetables and herbs for beginners.Use this information to help decide on the hydroponic system that is best suited for your garden and select plants that have the same temperature and pH requirements

Additional Notes
Other plants can be grown, such as mustard for green leaves, coriander for leaves, and amaranths for leaves. Maize can be grown for fodder mat, strawberry for planting material.Tomato, capsicum, chili, cucumber set fruits but are not economical to produce in hydroponic systems. Produce must should be ready for harvest within 15-25 days to be economical.
However, you can still grow them in your home hydroponic system.

Deep Root Veggies
Vegetables that need a lot of depth for roots are not recommended for beginners. This includes potatoes, carrots, turnips, etc.
For root crops, you need a substrate with sufficient length and high depth to support the roots. And these types of plants tend not to give as good results as they do in the soil.
If you have a large growing environment like a greenhouse or large patio, you can set up a more advanced system and grow sizable plants, root veggies, and other hard-to-grow vegetables.

Check pH & EC Regularly
It is important to check the actual pH & EC of the nutrient solution regularly. Electrical Connectivity (EC) is a measure of the salts in your system—that is, the level of nutrients in your system. EC should be kept between 1.2 and 2.0. Valuation of EC helps you to choose when should you replace or dilute the specific nutrient solutions with fresh water.
A pH test shows whether a substance is acidic or alkaline. The pH scale ranges from 0 to 14,with 0 being the most acidic, 14 the most alkaline, and 7 is the pH-neutral point. The optimal pH must be 5.5 to 6.5 (slightly acidic). Micro hydroponics nutrients reach the plants in a slightly acidic form, but pH below the optimal level causes micro nutrient toxicity.
EC and pH meters are affordable and often come as one dual meter

Pest and Disease Management
Based on the growth form and climatic condition, vegetables are attacked by various diseases and pests. Mealybugs, thrips, aphids and jassids are small sucking pests, injuring the hydroponic plants especially in the early stages of plant growth. This can be controlled by spraying with garlic, ginger and chili extract which can be prepared once in a week during the vegetative stage.