Note: You must install Zotero before you start. Make sure you either install the version for Firefox or the desktop version and a browser plug-in. You should also create a user. (To avoid mix-ups between accounts, you should never make more than one Zotero account. It is also advisable to avoid connecting other peoples' accounts to Zotero on a machine (or a user account) that you use for Zotero yourself.)
Zotero for Firefox:
Start by connecting your user to your library. In the Firefox version this is done by clicking the Zotero icon, then click on the gear and choose preferences... type in your user name and password.
In Firefox there is now a Z in the menu in the toolbar. Next to the Z, a symbol will appear depending on which kind of material you are looking at.
When you have installed Zotero, you can search for a book in Oria or an article in the database of your choice. When you are looking at an article, the toolbar will show an article icon next to the Zotero icon. To save the article to your library, simply click on the arrow next to the icon.
If you have a list of hits in an article database, you will see a folder next to the Zotero symbol. Clicking on the arrow gives you a list where you can check the articles you want to save, and thus save multiple articles at once.
Zotero for other browsers:
Zotero supports Chrome, Opera and Safari, in addition to Firefox. When you use one of the browser plug-ins, you start by connecting the plug-in to your account. In Chrome, this is done by opening the menu (the three horizontal lines in the toolbar) and choosing More Tools -> extensions. The plug-in then lets you choose to save your references to the desktop version or directly to the server. If you want to protect your library against a data crash, you should sync with both the desktop version and the server.
Once you have connected your account, you can keep searching for literature as usual. When you access an article, an article icon will show up, just like in Firefox, but in the Chrome plug-in, the icon is in the address field itself. As before, a folder icon will show if you are looking at a list of articles. If you press the article icon, you will get a message that your reference has been saved to your library.