To use Zotero's web interface, all you need to do is visit www.zotero.org and click the blue login option at the top right of the page.
Once you are logged in, you should see your library if you have anything in it. If you do not, you can navigate to it using the black tabs at the top of the page.
The Zotero web interface allows you to edit and make changes to all your citation information. If you have turned on the sync option for Zotero, you will be able to pull up PDFs and snapshots of websites. If you have not, the attachments you have in your Zotero Standalone will not sync to this site.
Zotero does not have an app for mobile use, but its web interface is mobile responsive, meaning it adjusts based on what size of screen you are using. As you can see, even using a mobile device, all the options are easy to access and change, just like in the regular web interface.