Short answer: email the webmaster, who will set it up and send back the login information.
Our most basic hosting plans don't include a database, so you might have to go up to the next plan. However if you're setting up a new active/scripted website, you probably need more space anyway.
More information: Sometimes phpMyAdmin is helpful to work with your database. We have a shared copy of this on each webserver. If you need it, please ask and we'll get access for you: this isn't set up by default.