The first thing you'll need is a good composting plan. You can start a compost pile in your yard if you have one, which will allow worms and microorganisms to get to work aerating your pile.
You'll need to keep the pile moist (think damp dish rag) and turn it every few weeks or look into a no-turn compost situation. The Sierra Club says compost forms best with a carbon to nitrogen ratio of 30:1. So you may need to up the carbon materials (which are usually brown, and include dry leaves, cardboard and peanut shells). Nitrogen waste is usually green and includes fresh leaves, lettuce and grass.
No yard? No problem. You can buy a bin or tumbler, which will also keep out insects and critters that are attracted to the compost. Need more tips? Get the dirt on composting (sorry) from the Sierra Club.