To use Zotero, you'll need to install two things:

1. The Zotero application itself
2. A connector to allow your browser to save citations to Zotero

Both of these are available from the Zotero download page.

Download and install Zotero from the Zotero website.

(There's a different version for each operating system: Windows, Mac or Linux.)

Connectors allow your web browser to save citations to your Zotero library.

The Zotero downloads page should automatically detect what browser you're using and give you a link.

Each browser has its own version of the Zotero connector, so if you use Chrome, Edge, Firefox and Safari you'll need to install all four.