After a recent talk, I was asked what could be done to increase the soil fertility in a vegetable garden where the soil had proven to be poor for growing food but great at weed production. The answer is to begin by pulling the weeds. Anyone interested in soil fertility should never poison the weeds and soil with herbicide. Cut the seeds off and put them in the garbage. I also remove the roots of the most noxious/persistent weeds - creeping bellflower for example - and put them in the garbage with the seeds. The stems and leaves can stay on the garden, or be put in the compost pile. The soil or compost microbes will make a healthy meal of the weeds and return their nutrients to the garden.
Next, if you can make aerobic compost tea (and everyone can, with a pail, dechlorinated water, an aquarium pump, and 4 cups of good compost), spray the bare soil with the tea. Then spread a couple of inches of finished compost over the entire garden, and scratch-till it into the top two or three inches of soil with a garden fork. You can buy organic compost, or use your own.
Use the garden fork to poke air holes into the soil, as deep as you can get the tines, and move the fork back and forth gently to loosen the soil. Never rototill, and don't chop, cut, or turn the soil with a spade, because that will harm or kill many of the beneficial fungi and bacteria already living in the soil. Your objective (and crucial role as a gardener) is to grow more soil microbes. It is the microbes that create the nutrients that feed your plants. The microbes also improve the structure of the soil so that it retains more water, nutrients, and carbon.
Next, spread some organic alfalfa pellets as a fertilizer. These will make a wide range of essential nutrients available to the plants over the growing period.
Finally, when you've planted the garden, cover any bare, unplanted areas with a couple of inches of fine-textured mulch, such as the partially-rotted leaves you saved from last fall.