If you've been invited to a calendar, you'll get an email with an invitation link. You simply click that invitation link to finish setting things up.
However, the invitation links only stay active for a limited time. If you've waited past the time and click the link, it won't work. The calendar administrator will need to send a new invitation.
If you click on the expired activation link, you'll see the email of the calendar administrator who sent the invitation. You can contact them and ask for a new invitation to be sent.