Download and install Zotero Standalone Library just as you would any other program. You will also need to install the browser and Microsoft Word Connectors to allow your browser to save items to your Zotero library.
There's a different version of the Zotero Standalone library for each operating system: Windows, Mac or Linux. When you go to the download site, the site will detect your operating system and browser, and prompt you to download the appropriate version of Zotero.
The windows download should include the Microsoft Word connector and the Zotero library software for Microsoft Windows. Remember to also grab the browser extension. All three parts (Zotero library, browser extension, and Word extension) should be working on your laptop in order to make full use of the Zotero system.