1. Basic Mailman Moderation
This document explains the basics of moderating a Mailman mailing list. It does not go into detail of all of the settings that are available, because that's an administrator's job and sometimes those are separate tasks.
The Mailman administration interface has a lot of settings that the average moderater need not worry about (and in fact, shouldn't mess with them.) What you need to know for on-going maintenence are the Membership Management and Administrative Requests.
The Membership Management page is to subscribe and unsubscribe members who for whatever reason are unable to do it themselves; it's pretty rare but it happens. Mailman also handles bounces from bad addresses automatically in most cases; however, some ISPs mail servers don't generate standard responses, so Mailman fails to handle them. Chief among the offenders is Hotmail. Mailman by default waits for 3 bounces before disabling a user's subscription; it is recomended that a moderator do the same.
The Administrative Requests page is to handle moderation. This should be pretty straight-forward.
Defer -- Leaves the message in the request queue untouched.
Approve -- Sends the message through.
Reject -- Removes the message from the queue and notifies the original sender of the rejection. There is a text field for changing the notification message. For an announcement list, it is recommended that messages sent in response to announcements be rejected but include a message advising the sender to post to a discussion-oriented list.
Discard -- Remove the message from the queue. Use this for spam or for messages where the sender has requested the message be removed.