I Had Trouble With This Too. BUT! I Found It.
Use FTP. Launch It Up. In Your Browser Go To Your cPanel Account. Then Go Down To The FTP Area And Click FTP Accounts. Configure The login Info With What's Given. And Your Password. Then Put The phpBB3 Extracted Folder On The Desktop. You can rename this to be whatever you want, because it will end up being
http://urlurlhere.domain.com/foldername/
You then upload the phpBB3 folder [Or whatever you named it] And Upload it to the Public_Html Folder. Then Wait. It's Like ~7 mB, so 5 Minutes or so. Then Go To This Address:
http://yoursubdomainhere.yourhosteddomain.com[or whatever extension]/phpBB3/install/index.php
EX: On mine it would be
http://blockis.exofire.net/phpBB3/install/index.php
If the folder was renamed to mainforum:
http://blockis.exofire.net/mainforum/install/index.php
There!
Now, for the hardpart. Entering the detailed stuff. Go to your cPanel account and create a mySQL Database. use the Database Wizard. Name it something. then go to the link the the left of the wizard. This is the MySQL Databse link. Click it. then it will list the databases with the username that you created. So keep going in the phpBB3 installation, then enter Localhost for the top text box. next, leave blank. next will be the Database name. So, For EX: blockis2_BB3 would be my Databaser that I created. then the user is blockis2_BB3 the same thing. yours may be different, check ont that mySQL databases page. It tells you everything you need to know.
Then enter your password. You should be good from then on.
Thanks, Blockis