Where can I find a list of federated institutions?

Answer...

OpenAthens maintains a listing of institutional members.

GÉANT maintains a listing of all federations and their members.

In theory, where an institution and a publisher/vendor are in the same federation, they can access the resources provided by that vendor (as long as they have a subscription). Each institution manages listings/catalogues of their subscriptions.

How does an institution indicate to all publishers that they would like federated authentication set up? 

This depends on the preference of the publisher/vendor. Many publishers request institutions e-mail their details (usually EntityID and scope) to set-up access. The WILEY online library is one example.

Some publishers/vendors have an administrative interface where an institution could sign-in and configure federated SSO, such as EBSCO.