How to back up:
The first thing you should do is backup everything. To do this, go to the admin panel on the forum and on the left side select "Backup Database," select "Full backup," "Gzip compress file," and "Start Backup."
It will take a couple of seconds and it should download a file (save the file, that's your backup of the data in the forum, eg. the posts, users and everything.)
Now it's time to backup the physical files. Just download them with your favorite ftp app, remember if you do forget something Dreamhost has backups in the .Snapshot directory located in your home folder.
Downloading the update:
Go here > http://prdownloads.sourceforge.net/phpbb/phpBB-2.0.13-files.zip?download and select a mirror and download the update. Unzip the download.
Installing the update:
Upload all of the files in that folder, overwrite files on the server (make sure not to overwrite folders though.
Upload the folders "install" and "contrib" to the server.
Load the file http://yoursite.com/forum/install/update_to_209.php
Make sure everything says it upgraded ok, if so then delete "install" and "contrib" from the server and your done