As mentioned earlier, gas fire pits are easier to clean than wood-burning models. In order to properly clean a wood-burning fire pit, you must first wait for the base and ashes to cool off. When you are certain it is safe, completely remove all the ashes inside of the fire pit. For safety reasons, store the ashes in a bucket and pour water over them and allow them to sit for several days. Then, you can dispose of them. Now that the base is free from any ashes, you can either use baking soda or a dishwashing detergent to clean the inside.
In more extreme cases, you can use a chimney cleaning product to remove and built-up substances. After you are done cleaning and are satisfied with the results, rinse down the base of the fire pit and dry it with a cloth. Wala, you now have a spick and span fire pit.