I'm researching the changes of social organization following Islam, and I'm trying to find material on the change of leadership.
I understand Mohammad installed a new Muslim government based off the philosophy of the Ummah, but I don't quite know how officials were selected, and where they were installed.
I'm not entirely sure what you mean by
Mohammad installed a new Muslim government based off the philosophy of the Ummah
if you expand on that it might be possible to give you additional information. A basic primary source that you might want to look at is the Constitution of Medina, and there are a number of secondary source essays on that text that outline why it was a such a radical departure from the tribal/kinship political structures that were prevalent at the time.