1) That's your web browser, and specifically Firefox — not your "computer" and not Word.
2) You have the Zotero web library loaded. You can't cite from that. You need the Zotero desktop app, which you can get from the download page.
3) The Z button in the Firefox toolbar is the Zotero Connector's "Save to Zotero" button (though I believe you would've had to have manually moved it after the Extensions button for it to be there). That doesn't have anything to do with citing. That's for saving items to your Zotero library.
4) On a normal webpage, that button should only show a Z if you haven't yet clicked on it since installing the extension or if something is wrong with your Zotero Connector installation. Normally that should change to show what can be saved from the current page. On the web library that should be a yellow folder icon.
5) Regardless, start by installing/opening the Zotero desktop app and syncing. The desktop app will install a Zotero toolbar into Word. That's what you use to cite.
Upgrade Storage
https://s3.amazonaws.com/zotero.org/images/forums/u6268433/xu2tz5v6220puy7tx7fk.png
1) That's your web browser, and specifically Firefox — not your "computer" and not Word.
2) You have the Zotero web library loaded. You can't cite from that. You need the Zotero desktop app, which you can get from the download page.
3) The Z button in the Firefox toolbar is the Zotero Connector's "Save to Zotero" button (though I believe you would've had to have manually moved it after the Extensions button for it to be there). That doesn't have anything to do with citing. That's for saving items to your Zotero library.
4) On a normal webpage, that button should only show a Z if you haven't yet clicked on it since installing the extension or if something is wrong with your Zotero Connector installation. Normally that should change to show what can be saved from the current page. On the web library that should be a yellow folder icon.
5) Regardless, start by installing/opening the Zotero desktop app and syncing. The desktop app will install a Zotero toolbar into Word. That's what you use to cite.