A steady program of soil building is like a steady program of physical conditioning. You'll get great results in the long run if you stick with it and don't go overboard right away.
Some things are soil amendments. They improve the soil's structure and ability to hold water, but don't change the soil's fertility. Organic matter, such as compost, is an excellent soil amendment.
Some things quickly change the soil's fertility, but don't do anything for structure. Liquid and granular chemical fertilizers are examples. So are some of the organic fertilizers like bone meal and blood meal. Ground limestone improves the soil's chemistry and ability to use fertilizers, but does not change structure.
Some things improve both structure and fertility. Manures are good examples. They also improve the life of the soil--the millions of earthworms and microscopic organisms that thrive in healthy soil and help plants process nutrients.
Soil amendments and fertilizers are better worked into the soil than parked on top of it.
Peat moss, for example, is a natural material that holds up to 20 times its weight in water. Spread two inches of peat moss on the garden bed and then turn it into the top six to eight inches of soil.
On top of the soil, peat moss will dry out. Water might run off and, or the wind might blow it away. It is not a good mulch.
Fresh sawdust is a poor soil amendment. It breaks down very slowly, and as it does, it robs the soil of nitrogen, one of the important plant fertilizers.
Granular chemical fertilizers should be worked into the soil, too. All the microbes and roots that the fertilizers benefit most live in the top few inches of soil.
There are many sources, some of them free, for materials that improve soil texture and fertilize at the same time. You can make your own compost. From region to region of the country, people work the local organic matter into their garden beds: autumn leaves, byproducts of apple processing, seaweed, buckwheat or peanut hulls, byproducts of winemaking, and so on. Check with local expert gardeners.
Manure is excellent for soil when composted, but has some bad features when fresh or uncomposted. The salts in fresh manure can burn plants just like any chemical fertilizer. There is no quicker way to bring unwanted weed seeds into a garden than to haul in uncomposted horse manure.
More and more people are interested in using natural or "organic" fertilizers instead of chemicals. Organic fertilizers are increasingly available in packaged blends. Most organic fertilizers do not have the high nitrogen-phosphorous-potassium (5-10-10) ratings of chemical fertilizers. They work gradually over a longer period of time, and do not cause fertilizer burn.
Most garden centers also carry organic products high in individual nutrients. For example:
Nitrogen for foliage growth: Blood meal, fish meal, fish emulsion, guano, hoof meal, horn dust, dried poultry manure, cottonseed meal.
Phosphorous for healthy root development (often used to fertilize flowering bulbs and for root crops such as beets and carrots): Bone meal, colloidal phosphate, phosphate rock.
Potassium (potash) for vigorous growth and disease resistance: Wood ash (use sparingly), kelp seaweed, granite dust, greensand, cocoa shell dust.
Gardeners often devise their own blends such as equal parts of peat moss and compost, or compost plus one of the ingredients high in individual nutrients to be used on specific crops.
Grass clippings are high in nitrogen. The best place for grass clippings is right on the lawn where they are cut, where they can provide between 20 and 50 percent of the lawn's nitrogen requirement.
Most yard wastes can be kept out of landfills and recycled right back into the soil either by composting or by chipping woody growth and using it as a mulch.