Most commercial fertilizers contain three key ingredients: Nitrogen
(N), Phosphorous (P), and Potassium (K). Trace elements, such as iron,
boron, chlorine, manganese, copper, and zinc are important too, but
rarely need to be supplemented, but are often included in very small
amounts, just in case. Other necessary elements such as carbon, hydrogen, and oxygen are taken from the air and water, not from the soil.
The N, P, and K are the three ingredients represented by the numbers in the fertilizer name. For example, an all-purpose fertilizer might be called 10-10-10 because all three elements are present in equal proportions.
N is most important for green growth. Later in the season, when your plants should be entering dormancy, green growth is unwanted, and nitrogen intake should be reduced. Also, too much nitrogen will prevent blooms from developing. N is water soluble and moves through the soil very quickly, so it must be replaced more often than the other elements, unless you are using a slow-release fertilizer.
Sources: All-purpose commercial fertilizer, Urea from microorganisms in the soil, Bloodmeal, manure, sewage leak (AKA that really green spot in the lawn over the septic tank)
This element promotes root growth, fruit ripening, and seed development, and it is especially important for very young plants and right before plants go into dormancy for winter. Phosphorous naturally occurs in composting organic matter in the soil.
Sources: All-purpose commercial fertilizer, earthworms, compost
Often called 'potash', this element is important for development of fruit and leaves, and it is responsible for the overall health of the plant. The most obvious sign of deficiency is scorched leaves.
Sources: All-purpose commercial fertilizer, wood ash, seaweed meal, compost, manure