All formal requirements for federations that want to become eduGAIN members and thus add Identity Providers and Service Provider to eduGAIN are described in the eduGAIN Constitution, Section 3 "eduGAIN Membership". In particular section 3.1 "Requirements for Participant Federations" lists the relevant points to consider.
The relevant extract is (please consult the eduGAIN Constitution for the current an up-to-date version):
Participant Federations MUST:
- Primarily serve the interests of the education and research sector.
- Provide a point of contact for their Members for dealing with technical issues.
- Provide processes for handling complaints and incidents involving their Members.
- Have a published Metadata registration practice statement.
- Follow the eduGAIN SAML 2.0 Metadata Profile if it decides to exchange the metadata of Entities via eduGAIN (“upstream metadata”).
If these requirements are met, a federation can initiate the "Joining Process" described in section 3.2. Some more details on this process are described on described on the page Process for an Identity Federation to Join eduGAIN.