phpBB upgrade instructions
Please read these instructions from top to bottom first to make sure you can do everything that is needed, it should be easy enough.
First, you will want to log in to your administration section of your phpBB2 board and scroll down to the "Backup Database" link. Click that and follow the instructions to make a backup.
Second, you will want to FTP (or shell) in, and download a copy of your "config.php". This file should be located in the "root" of your phpBB2 install, and should be surrounded by other phpbb-ish files. Once you have done this you will want to delete the contents of your phpBB2 folder. If you want, you can download an entire copy of this folder as well. (This is the Scary part! Don't worry, all of your settings are in the config.php and your MySQL database.)
Next, unzip the new phpBB2 files in to your old phpBB2 folder. If you are going to be using FTP, unzip the files on your computer, then FTP them up. Your phpBB2 board is almost there! Your directory should look pretty much the same as before, don't try visiting it in your web browser yet though! Now, upload your config.php file that you backed up before to your phpBB2 folder, you should get a warning about replacing the one on your server, which is currently empty. Go ahead and replace it.
Next edit this url to be your website and visit it:
Replacing the parts before /install/update_to_latest.php with where your old phpBB2 board is.
Once that has completed, you will need to go back to FTP (I promise, last step), and delete the folders called "install/" and "contrib/" out of your phpBB2 directory. Now you can visit your board again and all should be well! Go ahead and log in to your administration control panel and browser through your settings to see if anything looks amiss.
If you run into trouble, check out these articles from the PHPBB Knowledge Base: