Summarize:

Wait until the cleaning cycle is completely finished, the oven is cooled, and the door lock is disengaged to open the oven. Wipe down the inner surfaces of the oven with a damp cloth to complete the cleaning process. The high temperatures of the pyrolytic cleaning cycle carbonize food matter in the oven until it turns to a light ash, not unlike that from a cigarette or campfire. This makes it easy to sweep out with just a cloth. For after a steam-clean cycle, simply use a damp cloth to remove the softened and loosened food material from the surfaces of the oven. Clean the inner glass on the oven door, the oven racks, and any other elements with persistent stains using baking soda or your favorite cleaner. You can clean removable items while the self-cleaning cycle is completed. For an easy way to clean oven racks that must be removed from the oven before a self-clean, soak them in the bathtub with dishwasher detergent or apply baking soda and vinegar to remove built-up stains. Further clean the inside of the oven door only if the self-clean cycle has not removed all stains from it, and only after it has cooled completely from that cycle. Spot-clean in between self-cleaning cycles on your oven, but don't use abrasive materials like scrubbing brushes, rough sponges, or steel wool. These and harsh soaps will scratch away the pyrolytic coating, or the special enamel, that make self-cleaning possible. If you want to clean your oven by hand with cleaner, try a product that's intended for use with self-cleaning ovens, like Easy Off. Or use another mild cleaner or soap with a soft cloth or sponge. You should plan to use the self-cleaning feature regularly to avoid further need for cleaning. How often you perform this cycle will depend on your oven model, so consult the owner's manual or manufacturer.
Wipe down the cooled oven. Clean other parts as needed. Avoid hand-cleaning with abrasive material.