All you have to do is lay carpet remnants or several layers of newspaper over the area, anchor them with something heavy, like rocks or concrete blocks, and wait. In a few months, the grass and weeds underneath will be dead, and their decomposition will have added nutrients to the soil. Do this in the fall, and by spring you'll have a garden ready for planting. Some people substitute plastic for the carpet or newspaper, but Knorr recommends against that. It kills beneficial organisms like earthworms along with the weeds and grass, she says.
Good choices are hairy vetch or a combination of soybean and buckwheat.
Be sure to mow the cover crop before it goes to seed, then till it into the soil either in the fall or the following spring, she says. Buy from reputable producers, Miller recommends, and save yourself some heartache by choosing disease-resistant varieties, at least for the first year or so. When you're choosing transplants, she recommends looking for plants that are healthy, with no dark brown spots on the stems, or leaves that are falling off. Go through your starts before you plant, and discard any with spots or cracks, she says. Planting techniques depend on the vegetable you're growing, so follow the directions that come with the seed packet or plant.