To use Zotero on your mobile device, you can install a "Bookmarklet," a special link that saves items directly to your zotero.org account on the web.
There are a number of third-party apps, developed by groups other than Zotero's team at George Mason, that are aimed at mobile devices. These may allow you to add books by scanning ISBN barcodes, to download and read attachments, and to extract annotations. Zotero maintains a list of these third-party apps on their website.