During his rule, he nominally controlled as large a section of western Europe as anyone would until Napoleon. What military and administrative things did he do to make this possible?
One thing to keep in mind is that the Frankish Kingdom had long ruled over large parts of western Europe - see this map: https://upload.wikimedia.org/wikipedia/commons/thumb/1/16/Frankish_Empire_481_to_814-en.svg/1280px-Frankish_Empire_481_to_814-en.svg.png
Charlemagne's conquests on there are Saxony, Bavaria, the Lombard Kingdom, Carinthia, and the Spanish March - a substantial conquest, to be sure - but the bulk of his empire was already Frankish.
For actual description of the Carolingian organization, I'm no expert on it - but I found this answer by /u/MrMedievalist about some of those details. /u/GeorgiusFlorentius had this comment from a few years ago about the Frankish expansion from 450-800.