A plant's roots can be thought of as miners of the soil. Their primary function is to search out and provide the plant all of the water and nutrients necessary for growth and reproduction. In hydroponic gardening, the nutrients are presented directly to the roots: there is no need for the roots to wander and explore large areas looking for nutrition. Consequently, planting space can be used much more efficiently with hydroponics, compared to soil gardening.
Plants require a balance of at least 16 nutritional elements. Withhold one vital mineral from the plant and it will stunt its growth in some way. In ordinary gardening, the soil may test well on the necessary nutrients, but some of them may be present but not actually available to the plant in a usable form. Phosphate is commonly found in such a form. In order for the nutrients to do the plant some good, they should be present in a form usable by the plant. This is one of the main advantages of hydroponic gardening. You have complete control and consequently optimization of the nutrients presented to the plants. Hydroponic nutrients are divided into two basic classifications, macro-nutrients which are required by the plant in large quantities, and micro-nutrients, which the plant only needs small quantities of to thrive.
Generally, there will be additional trace elements, because the salts in which the various nutrients are supplied are not typically in an absolutely pure state. Some nutrients are naturally occurring in your water supply such as sodium or chlorine, but not necessarily in the right proportions. It is very important to have your water tested to ensure a proper balance of nutrients. The nutrients not in your water supply must be added in careful balance in amounts complimentary to the existing characteristics of your water supply. Hydroponic suppliers will have a variety of nutrients available in a premixed concentrate, or individual nutrients. To start off, premixed nutrient solutions are a safer bet; as you become more skilled you may want to investigate mixing your own nutrients.
The important thing to remember is balance. A balanced nutrient solution is delivered to the plant's roots periodically and the plant will take what it needs from that solution. The plant has to have all of these nutrients available all of the time. If for example, the potassium isn't there, the plant is going to take sodium in its place which could cause the leaves to burn from an excessive amount of sodium; when really the root of the problem is a deficiency of potassium. As another example, molybdenum is one of the required trace elements. The need for it is so minute (0.02 parts per million) that it is a bit dangerous to add it directly to the nutrient solution. If a molybdenum deficiency shows up, it will probably be supplied as an impurity of your other minerals, or the plant can also use the ionic structure of the nitrates to take care of the deficiency. It may be better not to take action.
It is also important to test the nutrient solution on a routine basis, as well as the plants to see what they are taking up. Generally speaking, nutrient levels should be checked every 10 days or so, and pH should be checked every 4-5 days. An alternative to checking the nutrient solution every 10 days, is to just replenish the nutrient solution every 10 days to ensure the nutrient balance is correct. The trees and shrubs outside your house will still enjoy the leftover nutrient solution.