How do I turn off register_globals in a dreamhost hosting account?
The quickest way is to run PHP5, which has register globals off by default.
You can set your domain to use PHP5 from the Domains -> Manage Domains -> Edit (under the webhosting column) screen(s) of the DH web control panel.
All right. Will that affect any current installations of, say, a CMS that is using the previous version of PHP and has a db runnning MySQL?
It could, but not necessarily - what CMS are you running, and is the version you are running PHP5 ready?