If you have no files at all, the easiest way is to:
1 - download your database
2 - Create a new installation of Phpbb (easiest to use the same version you used to run)
3 - Once you have a new bare bones forum, log into Phpmyadmin, or whatever you use to manage databases, and drop all the tables from the new install, leaving a completely empty db.
4 - Import your saved DB to the empty database. This will restore all users and posts etc
5 - If your old forum used any mods you can either reinstall them (any db tables should still be there), or use the Support Toolkit (download from phpBB) and run the database cleaner. This will remove all non standard tables leaving your db as if it was a clean install but retaining all posts, users etc.
When I lost all my forums, I chose this route and cleaned the database. I then updated the forum to the latest version, and reinstalled all styles and mods from scratch. It's probably not the easiest way to do things, but I knew I had everything bug free, up to date, and no bits of unused mod cluttering the database.