(This one's for you, Sabrina!)
Sheet mulching is touted as one of the easiest ways to reduce weeds in your yard or to get rid of a water-hungry lawn and replace it with something more drought-tolerant. (Solarization is a more extreme method that can rid an area of many fungal diseases, as well as weeds.)
To sheet mulch an area, trim any current plant growth to the lowest possible height, water the area (to provide for soil microbes) and then cover the area with cardboard. Be sure you don't used waxed cardboard used to ship produce. Once the cardboard is in place, cover it with tree trimmings, which can be gotten for free from most tree trimming companies. The cardboard blocks the sunlight to the weeds, preventing further growth.
Before you decide to sheet mulch, however, you need to understand that this is a temporary arrangement. Cardboard and newspaper attract termites and voles. Those layers also interfere with evaporation, percolation, and gas exchanges. They need to be removed as soon as the job is done.
Instead of sheet mulching, I urge you to call your local tree trimmer and ask for a free load of wood chips. The chips will provide all the benefits of sheet mulching, without the problems. A thick layer of wood chips 94 to 12") also improves soil structure and encourages the growth of valuable soil microorganisms. For free.
You can grow a surprising amount of food in your own yard. Ask me how!