How did Michael Scott become regional manager?

He is very childish and at times incompetent, but he can also connect with people in surprising ways.

Recall the episode when he & Andy go on a sales call (Traveling Salesman) and the man they speak with has a fishing photo on his desk. Michael strikes up a conversation about how he used to go fishing there as a kid and now he and the client [can't remember his name] have a connection. Naturally Andy ruins things but the important part to remember is that Michael is more than capable of being a people person.

Another great example is the Chili's episode (The Client) where Michael breaks down any defenses Christian may have with jokes and personal stories, in addition to some drinks and food. In the end, Michael is able to sell Christian on the fact that he "knows" Scranton.

So while Michael may be unconventional in many ways, he is capable of coming through when it counts, and I think this is the best explanation of how he became regional manager.