How are religious leaders chosen in your religion?

I recently asked a friend of mine about the Mormon religion, because some of my family members don’t like that Mitt Romney held some sort of position in his church. They think it is a problem of separation of church and state. My Mormon friend explained how it works:

We have a lay ministry in our church which means everyone who serves in a calling in the church does it voluntarily and without pay. That is what Mitt was referring to. Basically, you are invited to serve in a certain assignment, you accept and then you do that to the best of your ability until you are released. Then the cycle repeats. For example, right now I am a Seminary teacher. I don’t know how long I’ll be doing this but I’ll enjoy it while it lasts.

I asked if there was a heirarchy, and her reply was:

As for hierarchy, there isn’t one. One assignment might be as president of some organization, and the next could be teaching the 3-year-old class on Sundays. There’s lots of variety. Some assignments are only made to women or men, but that’s about as much hierarchy as there is.

I found that very interesting, and I think most people don’t know this about the Mormon religion.

So, I was curious about other religions. Please name the religion you are talking about (be specific, ie: Baptist, Methodist, Chassidic) and then describe how “leaders” of the congregation are assigned, hired, and how they study to be a leader. As far as I know Catholic Priests are assigned to churches, while other Christian churches hire a Minister? Not sure of the specifics. In Judaism I think anyone who has studied the right things can lead a congregation, I am not sure how they become a Rabbi for a specific synagogue.