To install Zotero, return to the Zotero homepage, www.zotero.org, and click the "download" button.
Please note that you will be installing TWO items: Zotero itself, and the browser connector(s) of your choice.
The Zotero downloads page should automatically detect what operating system and browser you're using and give you the correct link for both downloads.
Each browser has its own version of the Zotero connector, so if you use Chrome, Firefox and Safari you'll need to install all three from your chosen browser (i.e., you can't install the Safari connector from Chrome).