A "small, clean, hot fire" refers to a fire that's burning efficiently and not smoldering. This has nothing to do with the overall cleanliness of your pit, though it's never a bad idea to keep things neat and tidy. Ash buildup can hinder the pits ability to burn efficiently if it blocks airflow, but the presence of ashes in and of itself won't contribute to the buildup of creosote. Creosote, or stale smoke, or just an overall nasty, acrid flavor can be the result of incomplete combustion which you'll recognize by the thick, white billowy smoke. This smoke carries all those nasty components which the fire is hot enough to vaporize, but not to burn completely. A "clean" fire on the other hand, will produce smoke that is either thin and blue, or nearly invisible. This is the result of all (or most) of the volatile components in the wood burning off.
Think of it like an engine. An engine that's in tune is being fed the perfect mixture of fuel and air, resulting in nearly complete combustion in the cylinder and very little exhaust gas. One that's out of tune and running too rich will produce a tell tale stink from the exhaust and in extreme cases visible smoke. Your smoker works the same way. You have to feed it the proper mixture of fuel (wood and/or charcoal) and air. A smaller fire and a wide open intake vent will give you better tasting food than loading up on fuel and choking down the vents.
Depending on the type of pit you're running there are various methods to achieve this.