For cast iron ovens, you need to follow two processes.  The first is to remove any stuck food particles and the second is to reapply an oil coating.

Important: DO NOT USE SOAP to clean your Dutch oven.  The surface of the oven is porous and therefore will absorb the soap and taint your next cooking experience.

1. Removing food residue

Using using a plastic utensil or coarse sponge scrap off any remaining food residue and boil and inch or two of warm water in the oven.  It is not advisable to pour cold water into a very hot oven.  Let this sit near (not on) the cooling coals or briquettes to allow the food to break away from the bottom and sides.

After the oven has simmered for a while, use a green scrubby pad or similar to scrub it clean. 

Allow the oven to dry completely.  You may like to return it to near the warmth of the fire to assist this, but do not place it directly on the heat.

2. Reapplying oil coating

Wipe it dry and reapply a coating of oil (vegetable, peanut or olive oil) to the inside and outside of the oven and lid.  This will prevent rust forming.

3. Storing

Place a wadded up newspaper or paper towel inside the oven allowing some to protrude slightly over the sides.  The paper will allow a small gap between the lid and the oven to allow air to circulate.  Replace the lid on the oven and store in a good quality Dutch oven bag or wrap in a soft cloth.