You can download Zotero, both Mac and PC versions on the Zotero download page.
When it comes to using Zotero, please download the Zotero Standalone version. Zotero Standalone is a separate, browser-independent application.
One of Zotero's most compelling features is its ability to scrape bibliographic metadata from websites with a single click. In order to do this, Zotero Standalone needs to communicate with the browser you are using, which can be done by installing one of the Zotero Connectors:
If you've installed Zotero but are facing issues with Zotero, please visit the Zotero's support page. It contains useful FAQs and a comprehensive knowledge bank that should answer most of your issues.