First, you will need to register for an account with Zotero, which you can do here.
Choose your operating system and preferred browser, and download Zotero 5.0 and Zotero Connector.
So what did you just download?
Zotero 5.0 is a desktop application that you can use to create a personal library of resources for research, organization, and citation purposes.
Zotero Connector is installed in your browser, and allows you to save items into your Zotero library. Additionally, Zotero will in many cases gather the bibliographic information necessary to create citations, and allow you to cite in many different styles.
You can also log into your account online, where you can retrieve and organize items from your library. It is also possible to manually enter new resources, but you are unable to use Zotero Connector to retrieve online resources.