Wood burns best on a bed of ash which builds up on the grate of the stove. When cleaning your stove you should always retain a bed of ash and not remove all of it.
When your wood fire has built up a good bed of ash and embers, the airflow can be switched from below to above the fire for greater wood burning efficiency as this will promote an increased amount of secondary combustion (where the flue gases above the fire are reignited by an introduction of warmed air into the top of the firebox). The Hobbit clean burning stove is a good example of a wood stove with secondary combustion technology.
Efficient wood burning requires both a good dry fuel as well as a good supply of air. This will promote a visible and lively flame around the wood. Running your stove in this manner will result in a much cleaner flue. Running your stove slowly or shutting it down completely overnight will result in increased deposits in the flue, the stove and almost certainly a blackened window.
It should also be noted that constant refuelling of any wood stove will also be detrimental to an optimum efficient wood burning strategy. Better to let the fuel burn right down and then refuel. The wood takes time to heat up before ignition so will cause the stove to cool each time refuelling takes place.
Visit this video to see a stove being refuelled.