Create an "Unapproved" role in YAF. Assign the "Is Start" flag to that role (and remove from the "Registered" role).
Make the unapproved role have the same forum permissions (Access Masks) as the Guest role. Set the email setting in the Board Settings so when a user registers it emails you to notify.
When they register search for "Unapproved" users in the user editor and change them to Registered role manually (if you want to approve them).