How did Ghengis Khan establish his empire?
He gave unaligned Mongols a simple and appealing code to live by.
Temugin was a small-time regional khan and the son of another khan. He realized early on that power isn't conferred on anyone by a greater authority or power; it is simply something that a man of destiny takes. The Mongols had several such khans among them, and plenty of unaligned bandits and such who didn't even realize they were looking for a greater meaning in life.
As Temujun became Genghis Khan, he gave his followers two rules to live by (which was two more than most of them had ever had): Don't hurt women and children, and never betray your khan. It gave this barbarian horde a focus and motivation they had been lacking, and it motivated them to conquer most of northern and western Asia (and beyond, although Genghis died before the Golden Horde reached Russia).
His grandson, Kublai Khan, expanded the empire southward into China and for a couple of centuries, this was geographically the largest political entity in history. It was dissolved by infighting and fragmentation; half the known world is a little too big to competently maintain.