The process is outlined here by Jeff. Basically if someone is constantly being flagged as offensive or spam by other users, they are sent an email by a moderator. If the behavior does not change, the user is suspended. This is only done in extremely rare cases (I've only seen it once - not that I actively look for it though)
It is not done anonymously, it is done by a mod and there is notification given via private email to the offending user.