First, you're going to need to download Zotero from www.zotero.org. You should first download the desktop application and then add the browser extension to your preferred browser(s).
If you are planning to use Zotero with a word processor such as Microsoft Word, the necessary plugins should be automatically installed when you install the Zotero desktop application. If this does not happen, or if you need to reinstall the plugins for some reason, you can follow the instructions on their word processor plugin installation page.
After you install the Zotero desktop app and the Zotero Connector, you will need to set up your preferences to allow for syncing and cloud storage of your citations. The first step is to register for a free Zotero account. You can do this on the Zotero website and you can use your personal email address if you prefer.
Once you have created an account, you can return to the desktop application and sign in. Head to the desktop section of this guide to under how to sign in to the application as well as become familiar with the applications layout structure.