I'm going to assume that you have PHP and MySQL. To get your forum started, do this:
1) Download PHPBB:
phpBB • Downloads
2) Extract it and upload it to a directory on your server where you want it (for instance .../forums/)
3) Create a database for PHPBB. You will also need a username for PHPBB to use, and it will need full access to the database. I can't explain how to do this because that depends on the host and control panel you are using.
4) Run install.php (located in your PHPBB directory, in the install directory- for instance .../forums/install/install.php)
5) What you enter here is pretty obvious and depends on your server settings, database name, username, password, mysql version, etc...
Then once you are finished, it will auto install, and you are all set.