If you have access to the MySQL database, you can export the contents of that to a .sql file and, once on the new server, import the sql file. This is easily done on phpMyAdmin if you have access to it, or you can do it manually. When you do this, you can literally copy and paste all the old files from the old server to the new server, then import the sql file, and, after making some modifications to the config files in order to accomodate the new mysql server, it'll be the exact same forum. If this is what you want, that is.
If you don't have access to the db, there's not much you can do.
Post edited at 3:50 pm on June 23, 2008 by matto
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"Say what you like about the tenets of National Socialism, Dude,
at least it's an ethos."
--Walter Sobchak