Do you know what version of the message board software you have? The old and new board version will have to match, or you will get database errors.
[b]EDIT: I just realized you meant Vanilla 2 the board software (I have not heard of it before)...
I assume you've read through this: http://vanillaforums.org/docs/installation
But, your board already has a database, so the general info that follows should still be helpful for migrating...[/b]
IS a database ready to go at DH?
Dreamhost handles databases a bit differently than some other hosts, You must go through the panel to create a new database. In the panel, you create a sub-domain for your database(s). You can then create a new database, user and password. You can then use phpmyadmin to log into your database and import your backup.
If it is too big, you'll need to use the shell.
Here's some more info on a few approaches: http://wiki.dreamhost.com/Migrate_MySQL
Now, to the board files:
Set up your domain if you haven't already to use the version of php that works best with the message board software you are using (if it is an older version, you may need to use an older version of php...).
Log into your server root using ftp or sftp and upload the board files.
Find the board configuration file. You will set the new database info and location there, you may have to look around for it and, if you cannot find a config file, and depending on what board software you are using, you may have to change these credentials from within the database itself. Browse the database rows for it.
Again, depending on the board software and version, You may also have to put in the absolute path to your server files somewhere in the config. It would be something like: username/home/yourdomain.com
where username is the user who you selected in the DH panel to run the domain, the ftp/shell user.
Once the configuration can find the database, the board index should appear.
You mention you are getting errors, so not sure which of these steps you have already implemented or where it is breaking down...