Many thanks for your help. It was wholly unclear in the DH wiki how to do this, and any searches for DNS inevitably led to information only on how to transfer domain registration.
In the case anyone else comes across this issue, here's the solution:
Now you will need to add the domain to your hosting. You can do this in the panel on the Manage Domains page (Domains > Manage Domains) by clicking the + Add New Domain/Sub-Domain. Enter the domain name and the appropriate information. It takes about 1-3 days for the DNS to
propagate across the entire Internet.
NOTE: The upshot of this is that if, as in my case, you created a site (or blog) using the yoursite.dreamhosters.com subdomain listed in the Manage Domains page, you'll have to transfer all of that content to the new Domain was added in the directions above. For Wordpress users, that means a new installation of Wordpress, exporting the content from the old blog, and importing it into the new one.