The Bris (technically, the Milah = Circumcision) has a few stages that a Mohel must follow in order to produce a "Kosher Bris" and, hopefully a nice circumcision as well.
We have already "reposted" the methods of circumcision (2nd link shared on that page)
The day of the bris, the baby should stop eating a small time before the moment of circumcision, to avoid the possibility of his spitting up and choking will crying.
People stand when the baby is brought in to the room
This basically describes the ceremony that everyone sees
This is what circumcision looks like (in words, no photos, except of a banana)