...
Enabling a service for eduGAIN login is accomplished by joining an existing eduGAIN member federation and registering a Service Provider with this federation. The member federation then, following its own procedures, exposes the Service Provider to the rest of the eduGAIN federations and their entities.
Which (eduGAIN) federation to join
Joining eduGAIN means joining an eduGAIN member federation. But which one to join? There is no strict rule which federation to join. But one reasonable option should be to contact the national federation of the country where the Service Provider’s organisation is located or where the service is geographically operated (i.e. where its operators are located). This offers multiple benefits, such as ease of collaboration and access to documentation because of common shared native language, shared groups of interested prospective users, etc.
...
Consider also that in some cases a service is already available via eduGAIN without you knowing it. This is sometime the case for publisher services that in pre-eduGAIN times were often registered with many national federations. When one of those national federations joined eduGAIN and exported their services, they become availabel available through eduGAIN as well. To verify if your service is already exported to eduGAIN look it up in the eduGAIN Entity Database:
...
To register the Service Provider (SP) with a federation, one typically has to provide its SAML2 metadata to the federation operator. If you don’t have metadata about your SP yet, you might need to generate/compose it first. Shibboleth can generate SAML2 metadata about itself, just try accessing https://your.host.org/Shibboleth.sso/Metadata
SimpleSAML PHP SimpleSAMLphp has a similar feature. Just open the URL https://your.host.org/simplesaml/module.php/saml/sp/metadata.php/default-sp
...