Once your garden is planted, it will generate large amounts of organic waste--material you can easily turn into rich compost and return to the soil. The simplest composting method is the familiar backyard pile, but you can also use various kinds of bins or, if your space is extremely limited, even a box of worms.
A simple compost pile
For this method, you'll need a space about 10 feet square. Divide the area roughly in half. On one side, alternate 6-inch-thick layers of "green" and "brown" material. Green material includes grass clippings, soft shrub cuttings (chop up any large pieces), some pulled weeds, and the like; brown material includes dry leaves, used potting soil, wood chips, and sawdust. This fifty-fifty green-brown mixture helps maintain the carbon-nitrogen ratio optimal for decomposition. Aim for a pile that's about knee-high. If you're short on green material, add alfalfa pellets; if you're short on brown, add straw (not hay, which contains weed seeds). Both are available at feed stores.
Once a week, mix and turn the pile, moving it to the other side of the space. In about a month, you'll have coarse compost. If you want a finer texture, continue mixing and turning for another month or two. In dry weather, hose the pile down when you turn it; it should be kept as moist as a squeezed-out sponge.
Note that this method requires you to have sufficient material for the entire pile at one time; you can't add new material until the current batch is finished.