Installing Visual Studio Code is as simple as downloading the platform installer that is specific to your operating system. You can visit https://code.visualstudio.com/ and the site should pick up which operating system you're using and display a download button.
For example, since I'm visiting the site from a Windows PC, it automatically displays a Download for Windows button:
If you need to download it for either Linux or OS X, scroll to the bottom of the page and click on the appropriate download button:
For complete instructions on getting up and running with Visual Studio Code on Mac OS X, Linux, or Windows, visit http://code.visualstudio.com/Docs/editor/setup.