Download Zotero from zotero.org by clicking on the Download button. Zotero is available for Mac, Windows, and Linux operating systems.
You'll want to download the standalone Zotero application as well as the Zotero Connector for you browser of choice (Chrome, Firefox, Safari, Opera--and yes, you can download Zotero Connector for multiple browsers!)
Zotero is already installed on public Macs and Windows machines across campus. When you log into a Wellesley computer, you'll just open up Zotero, log in to your Zotero account, and sync your Zotero account to that machine before you get started. You'll have to do this for each new Wellesley computer you sit at, but don't worry, it's not hard!