Apropos of last week's peaceful transfer of power in Washington, I recommend this weblog entry, which helps explain the origin of the term "inauguration," and gives a thorough description of the various kinds of divination practiced by the Roman republic.
According to the author, augury (the root-word in question) was not actually divination - it was instead a way to determine, by observing the flight of birds in specified sectors of the sky (or ostentaria), whether the gods approved of a proposed course of action. When a new public official was elected or appointed, the Romans used augures, haruspices - the readers of entrails - and fulgatores (lightning-interpreters) to determine whether his selection was well-omened, and thus legitimate.
The article is a bit long, but worth reading - it explains, among other things, how to conduct an augury, what the various terms associated with the practice were, what birds' flight or calls were important, and how the Romans resolved contradictory omens. The link is courtesy of the daybook of conservative writer Jerry Pournelle, who is trying to be a good sport about Barack Obama's inauguration.