When you click the link to watch a forum, you'll see an overlay like this:
Notification-less watching options may be expanded in the future (such as with indications on the new threads list).
Notifications work identically to thread watching notifications: you'll only receive one about a thread until you view it on the forum.
Like threads, you can manage your watched forums in bulk via a dedicated page. This can also be used to simply filter only to forums you're interested in.
Administrators can also limit the type of notifications that can be triggered when watching a forum:
This can be useful to reduce the number of notifications that will be triggered on particularly busy forums.