Dont have to outnumber them at all. Just being superior in the weapon department.
The outcome of the clone war might give us the clues to how they controlled the galaxies.
To me it looks like the separatists are mostly alien worlds, well the clone war will drain their resources and leave them beat and war thorn.
The entire galaxy probably are war thorn so this may make it easier to accept a military force to restore order (in comes the empire). Way to late will they understand the real consequence of such an action, but not only to late to understand, to weak to protest too. Only a few cell scattered around fight back, not really too well organized to be an immediate threat to the Empire
The galaxy seem to have been too dependent on the Jedi`s to sort out the occurring disputes that pooped up from time to time, without the Jedis the protection are gone.
The thing that happens in the OT is that more system rally to the rebel alliance cause though so the resistance is growing