The mobile version of zotero.org allows you to access and edit your Zotero library on your tablet or mobile phone.
The Zotero Bookmarklet allows you to save items from your mobile device's browser directly to your zotero.org account.
While there are no official Zotero apps for mobile devices, there are several third party solutions.
For iPads and iPhones...
For Android devices...
You can use Zotero on the iPad browser by installing a "Bookmarklet," a special link that saves items directly to your Zotero account on the web.
You must have a Zotero account, and your iPad must be online, to use Zotero.
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.