There are no official Zotero apps for mobile devices, however setting up the Zotero "Bookmarklet" in Safari and using the PaperShip app can allow you to use most of the features of Zotero. You must have a Zotero account, and your iPad must be online, to use Zotero.
Registering a user account allows you to sync your Zotero library between devices. Use a non-GC personal email address, you can keep this account long after graduation.
Download and install PaperShip for Mendeley & Zotero from the Apple App Store.
The "Bookmarklet," a special link that saves items directly to your Zotero account on the web. Open zotero.org/downloadbookmarklet in Safari and bookmark it. Then, click “iPhone/iPad” and copy the code from the text box on the page.
Edit the bookmark you just created. Then change the bookmark name to "Save to Zotero".
Paste the code from the text box as the URL for the bookmark.
When you're on a page with a citation, select the Save to Zotero bookmark. The iPad browser will save the citation directly to your Zotero library online.
Using your Zotero login you can access your saved citations and references from the PaperShip app, as well as any any computer on which Zotero is installed.
To ensure that your PaperShip library is being synced with Zotero.org (in the 'cloud'):