Backyard composting can be as simple as layering your kitchen scraps with fall leaves in a corner of your yard. Stocking up on raked leaves from your neighborhood in the fall can supply your composting needs for the year.
Monitoring the moisture content, frequent turning of the pile, and attention to what is added and in what proportions will hasten its break down into compost.
Ed Rishell, Master Gardener, has written a comprehensive guide for backyard composting for the Virginia Cooperative Extension here.
Pet wastes may not be safely composted in open backyard compost piles especially if intended for vegetable gardens. Industrial composting operations achieve the high heat needed to kill off potential pathogens in these wastes. An alternative is to dispose of them in lined or unlined backyard holes where they can decompose more safely.
Www.cityfarmer.info provides some ideas for this here and by clicking on the painted dog image above.
More here from the Recycling and Environmental Action Planning Society out of Prince George, B.C.