All plants need nutrients to supply them with the elements needed for vital biochemical processes.
Nitrogen (N), phosphorus (P) and potassium (K) are the top three generally listed, but there are more than a dozen others. Magnesium (Mg), iron (Fe), calcium (Ca) and several more perform essential roles in the life of hydroponic plants, just as they do in soil-based gardens.
Nitrogen is used by growing leaves. But despite the fact that the air is about 79% nitrogen, plants need it in the form of a supplement. The N2 molecule in air is very stable and plants don't break it apart to use single nitrogen atoms. Phosphorus is essential to root growth. Potassium aids in disease resistance owing to its role in enzyme formation.
The other elements perform a variety of functions. Calcium, for example, is a large component of cell walls and also helps deliver ions to various parts of the plant. Chlorine (Cl) is a component of chlorophyll, an important participant in photosynthesis. Iron is essential to the hemoglobin molecule, which is formed by plants as well as animals, where it helps transport oxygen needed for cellular respiration.
Pre-made solutions are the easiest to work with to supply all the needed elements. As with any compound, dosage is important. For very young plants, such as small cuttings or those that are just germinating, 1/3 teaspoon of calcium nitrate dissolved in a gallon of water is about right, for example. Plants that are flowering will require more, about 3/4 teaspoon.
Water and temperature conditions are important factors, as well, when feeding your plants. Any solution should be fed at room temperature, which should also be the temperature of any water used in hydroponic gardens.
Dry plants should not be fed nutrients. Nitrogen burning is possible. That's rarely a problem with hydroponics, but one 'branch' known as aeroponics, where the plants are grown in air, can suffer that problem.
Allowing any water to stand overnight will help evaporate any excess chlorine from home water sources. Mineralized water is preferable to distilled since it will contain calcium and other useful elements.
Regulate the pH to keep it as near neutral as possible. As plants take up nutrients they'll tend to make the water alkaline. Add tiny small amounts of sulfuric acid to move it back to neutral. Sodium hydroxide will help shift excessively acidic water back to a neutral pH. Testing kits are available to accurately measure the pH of your hydroponic water.
Hydroponically grown plants are more sensitive to nutrient levels and less able to self-regulate than those in soil-based gardens. In soil, for example, they can take up or shed compounds. Releasing compounds into the water medium doesn't move them away from the plant. The hydroponic gardener will need to exercise more care to keep plants healthy.