Once you're at the login page, click "register for a free account" just above the login boxes.
Once you've gotten to the registration page, you'll create a username and password and link your account to an email address. You do not have to link your Zotero account to your Fairfield email address. If you do choose to do that, just make sure to link another email address to your account sometime before you graduate.
Zotero is free and gives you 300 MB of storage to start with. Unless you're saving a massive amount of PDFs to your account, you may never even fill that up. However, you can also upgrade your storage with a yearly subscription.