Well, while leaving out quite a few things, here: a general overview of how I've got mine setup. I imagine it's fairly similar to how others do it:
config
General configuration settings
groups
groupid (auto_increment primary key)
Stores settings and permissions for each user group.
users
userid (auto_increment primary key)
groupid - Points to the user's group
Other fields like username, password, email, etc. to store user information.
forums
forumid (auto_increment primary key)
name, description, etc. to store forum info
threads
threadid (auto_increment primary key)
forumid - Points to the forum that the thread is in
subject, iconid, etc. to store thread info
posts
postid (auto_increment primary key)
threadid - Points to the thread that the post is in
userid, message, subject, etc. to store information about the post
This is not even close to a complete list, but if you need more info about how to setup the tables, just ask.