I'll do my best to explain how it works, but let me know if someone wants to correct or add to this.
Basically you build a fire in the fire pit using lump charcoal and chunks of whatever wood you want to smoke with.
Next, you insert a ceramic plate setter that can be seen in one of my last pictures. This ceramic piece is used to block the direct heat from the coals in order to create an indirect heat source similar to a bbq pit with an external firebox.
Then you place a drip catch pan on top of the plate setter and finally place the grill grate on top of that.
By adjusting the vents on the bottom and top, the airflow to the firebox can be increased or decreased. This airflow directly controls the speed of combustion thus the temperature of the grill.
Fido recommends that the top vent be kept closed (or near closed) during smoking in order to keep a good head of smoke in the cooker.
I have noticed that because the firebox is not external, almost all of the heat produced by the fire is contained in the egg which makes it more fuel efficient (little to no fire stoking) but less smoke efficient (slower fire produces less smoke). In order to compensate for the small quantity of smoke, I did not cover my brisket throughout its 13 hour cooking time. In my dad's big pit, it might have been over smoked, but in the BGE it wasn't even close.
The Large BGE weighs roughly 200 lbs, which is a lot of thermal mass. As long as the vent holes in the firebox are not plugged with ash, a consistent flow of air should pass from bottom to top. In my experience (which is pretty limited) using a clean burning lump charcoal allowed me to maintain 250deg for the majority of the cooking process without any adjustments.