Zotero is free, but use your uniarts e-mail address when you register to Zotero. Uniarts has a Zotero Institution subscription, and Uniarts members have unlimited personal and group cloud storage for reference attachments (the full-texts as PDFs). The free version without institutional subscription has limited storage.
Install Zotero to your computer (for Uniarts Mac computers Zotero is available from the Zappa environment). If you are asked for admin credentials while installing and you don't have any, just click "No", and the installation should begin anyway.
Choose "Standard" as the Setup Type, unless you know what you are doing. The Word plugin is also installed at the same time.
After the installation is finished, synchronize Zotero with your account: login to your account in Zotero's Sync tab.
Install Zotero Connector to your browser as well and you can save references with a single click. Zotero Connector is automatically installed to Safari when you install Zotero to your computer, but you need to activate it in Safari's settings: Settings > Extensions.
See Save and edit references tab for more information about saving references.
If you registered to Zotero with some other email address than Uniarts's, you might have to sync your files after changing your email address, to get unlimited cloud storage for files. Click the circular arrow in the top right corner in Zotero to sync.
Zotero Connector for Chrome might not be visible on the browser after you install it. Go to the extensions menu in Chrome and pin Zotero Connector as shown in the image below.
Sometimes Zotero tries to redirect you to electronic sources which Uniarts has a subscription to via a proxy (at Uniarts it's a service called EZproxy). Sometimes this redirecting can cause issues and you might have to disable it. Click the Zotero Connector icon on your browser and choose Preferences: on the Proxies tab disable the option Enable proxy redirection.