Cover crops have been/are being used as organic mulches in crop production systems in order to increase soil organic matter, improve soil structure, conserve water and reduce erosion. Cover crops can also suppress weeds by serving as a physical barrier to seedling emergence, inhibiting seed germination via reduced light transmittance, through the release of allelopathic chemicals, and by preventing herbicide loss.
Attached is a video from the University of Georgia describing how to mange and roll rye (not ryegrass) for Palmer amaranth control in a cotton conservation-tillage system. Although much of the information (i.e. herbicide recommendations) may seem specific to the eastern coastal plain, the clip does provide a very good overview about the advantages and difficulties of cover cropping.
Video: Rolling Rye to Control Tough Weeds
For more information, just search for 'cover crops' on YouTube or visit these webpages from UC Davis, Cornell, Ohio State, Purdue, and Penn State (among many others). If you are looking for 'the personal touch', lots of growers have been sharing their experiences with cover crops in their blogs or on Twitter. Cover cropping may not be physically or economically feasible for every production programs; your cooperative extension agent can help you make that decision. Advisers generally recommend starting off small to become familiar with the intricacies of the system. Many growers that have transitioned to cover cropping can report that practice does make perfect, and mistakes are often the best teachers!