As you may have noticed, managing the different elements listed in "getting started" (structure, pH & nutrients) are closely linked together. You may have also noticed the answer to correcting the different elements of your soil has been - ADD ORGANIC MATTER!
Well...that seems to be the case, organic matter is the only amendment that aids both the fertility and texture of the soil, and helps neutralize pH. However, in order for your garden to receive the nutrients that result in "maximum gardening yield" you will want to add fertilizer even with a well managed soil. Whether you use organic or synthetic is up to you!
Why do we need fertilizers? The plant absorbs mineral elements and water from the soil and carbon dioxide gas from the air. The elements most frequently deficient include those normally present in fertilizers—nitrogen (N), phosphorus (P), and potassium (K). The ratio of N-P-K such as 15-15-15 is what you will see on the label. Another important nutrient element—calcium—is added in fertilizers. Other elements that may be deficient in some soils for some crops include magnesium, boron, manganese, copper, zinc, iron, molybdenum, and sulfur.
All soils, even those never cultivated, differ widely in their content of plant nutrients. Soils lose available nutrients through erosion, leaching or washing out, and the harvesting of crops. Some of these losses are regained through the weathering of minerals, rainfall, the action of soil organisms from subsoil with or without erosion, and by the upward movement of ground water.
Deficiencies of plant nutrients in soil must be corrected if the soil is to produce adequately. Fertilizers and manures are added for this reason and also to increase plant growth. Source: Oklahoma Cooperative Extension.
If you had a complete soil test that should help you determine which fertilizer your garden needs. If not, you can start off by purchasing specific fertilizers for your plant type (i.e. turf vs. trees) or use a multi-use fertilizer. The best advice is to make an educated guess and go on trial and error from there.