ok, how you work with dreamweaver at home (are you running local PHP?) will determine how you upoad you files/HTML to Dreamhost -- no relation
If you want to see/edit phpBB through Dreamweaver, you need to install and run it on your home computer -- you need the whole LAMP set-up.
To get your html and images that you've created in Dreamweaver to Dreamhost use FTP, either through Dreamweaver or with an FTP program. Your phpBB will be in a sub-directory, your front section (HTML files) can be at the root of your domain.
Generally, you manage your forum online, through the Administration panel. You can find (and customise) various templates to match phpBB to your site.