If you don’t have an edu-ID account yet, go to the edu-ID website and click the “Create an account” button :

You then fill in the form to create your account.
You will also need to set a password for your edu-ID account. For security reasons, please do not reuse your EPFL password.

After creating your account with your personal email, you will receive a request to confirm your email address.
Then you can connect to your account in order to complete it and especially to link it to EPFL by clicking on the plus + on the Organizational Identity line of the Linked Identities section :

A dialog box will then allow you to choose the organization EPFL – EPFL Lausanne :

then after clicking on the Continue.
You’ll be redirected to the eduid.epfl.ch page in order to link your edu-ID to the EPFL organisation.