"Solarization" is the term for the process of killing weeds and other bad things in your soil (ground fungus anyone?) by trapping the sun's heat. By laying plastic over the ground you both block the weeds from getting light and heat the soil underneath to inhospitable temperatures.
The best part is it's pretty easy - all you have to do is keep the ground covered for a few months. Yes, it's ugly, but we think the end results of a weed and chemical free garden (without spending literally months weeding by hand every weekend) are worth it.
Any other non-toxic gardening advice out there?