Zotero can be installed on your desktop or used online in a web browser. To use all of the functions the tool offers, it is suggested to download and install the desktop version.
If you are just looking for a tool to create quick citations, check out Zoterobib a simpler citation tool by Zotero.
See the "Setting Up Zotero" link below for instructions on how to set up Zotero on your desktop.