Post a 4000 BC save and you'll be bound to get some shadow games which will show you how to dominate at monarch. It was a moderately tough jump from prince, because warrior rushing is no longer an option (unless you're HC), but all in all, the AI bonuses aren't significant enough at that level.
The usual keys, plenty of workers, city specialization, prioritizing the right wonders for the map/civ, and then adding in better diplo should be plenty to succeed easily at monarch.
The usual keys, plenty of workers, city specialization, prioritizing the right wonders for the map/civ, and then adding in better diplo should be plenty to succeed easily at monarch.