What most of these site do is use an open source or inexpensive bulletin board software. Many exist out there.
Once you have found the BBS software that you like, you have to find a HSP (hosting service provider) that will support the requirements of the BBS. For example, ehmac uses PHP and a backend database (with a few other pieces of software).
Now some HSP have BBS software pre setup.
Then, to be you can modify the look of the BBS in the admin section and also adding your own graphics.
whats wrong with PHPBB?
Its a solid board package that also works well , and it sfree, has many mods and skins, and all kinds of tweaks you can do to it.
1000s of people use it!
check it out http://www.phpbb.com