i only know how to do it via ftp. you basically copy the phpbb folder onto the ftp. then go to www.yourdomain.com/phpBB2/install/install.php
thats if you have phpbb2, and its different for phpBB3, the /phpBB2 may be different, depending on what you named the folder.
then just go through the steps.
yea. your hosting should give you a certain amount of db's. on mine i just login to their cpanel with my username and password then theres a mysql db manager. phpBB wont work without one