The three prime nutrients are on most fertilizer bags in the order Nitrogen, Phosphorus and Potassium or NPK. Each number will tell you how much of each chemical the package contains. A balanced fertilizer will have all three numbers the same. In general the nitrogen is needed for formation of chlorophyll and is associated with green growth such as in lawns and leaves; phosphorus is needed for cell division and encourages strong root development and potassium is good from fruit set and overall vigor. Most soils contain sufficient phosphorus and potassium to support most plants, but particularly in an intensive vegetable garden, you will need to add some for maximum production. Note that phosphorus is banned in some states so check the site before you make your final decision.
Synthetic fertilizers use urea for the major nitrogen source and other chemical compounds. Organic sources for nutrients include dried blood or blood meal for nitrogen; bone meal for phosphorus and wood ashes are good source of potassium.
Balanced fertilizers contain a mix of the main three elements but also include many of the secondary nutrients that are just as necessary for good growth, but are only needed in very small amounts. Mixing several different natural products together is one way to get this overall well balanced fertilizer.
Vegetarian fertilizers do not come from animal products but they can still be a great source of nutrients. Common options include alfalfa for all around health of the plant and soil, cottonseed for nitrogen, rock phosphate for phosphorus and kelp for potassium.
Always apply fertilizers according to the instructions on the container. Some formulations can be sprayed directly onto leaves, others need to be diluted or applied to the side of the plant. Using a fertilizer that is too strong, even though it is organic, can kill the plant rather than help it.
A good general application of compost and well balanced fertilizer can give a boost to rapid spring growth. A second application for tomatoes, beans and other vegetables is also a good idea to maximize your harvest.
By using fertilizers correctly and at the right time, you will have a healthy garden all year long.