You first need to copy developpement files from dev to prod. In normal cases that should be :
- design/example
- settings/siteaccess
- settings/override - extension
provided you haven't done any kernel changes, that should do.
Next step is to do just as you said : transfer your dev database onto your prod server.
Make sure to configure the database settings and such things in order to suit the new server requirements and login policies.
You'll also want to take the var directory, which must be completely in sync with the database (copied at the same instant, or copied while the database is locked down). And, of course, you'll need to change your site.ini files to match the production server environment.