For your phpBB forum you will have a MySQL database for example 'phpBB'. Your config.php will have the settings for the location of the database (hostname) the name of the database (phpBB) the database user (some_user) and the users password (topsecret_password)
With your old site they probably used the hostname 'localhost' for the database location but under the DreamHost way of the Jedi you have a Hostname as the hostname. e.g mydatabase.example.com.
So you just need to first set up your database using the DreamHost Panel to create a database. You can re-use the details from your old site phpBB for database name,user and password.
Once the database hostname has propagated (instant to hours!!) you can install your old database either from phpmyadmin (but you will need to chop the database sql file into sub 7MB lumps because of the PHP limit of 7MB. Best call it 5MB.
Or if you are comfortable with accessing your shell with SSH then you could use command line mysql and use:-
mysql -u username -ppassword -h hostname.example.com database_name < bigwhopping.sql
Which should hopefully re-create your old database.
You can than install your phpBB files updating your config.php with the four new items (remember do not use 'localhost' anywhere, always use your mysql hostname).
That should be it.
Since phpBB is a DreamHost one click install you could use that and initially set up a database/hostname/user/password layout which is not the same as your old set up. When it has all been installed you can then change your config.php to reflect your bigwhopper database.
Opinions are my own views, not DreamHosts'.
I am NOT a DreamHost employee OK!! :@
You act on my advice at your own risk!