The browser extension is the glue between the Web Player on your web page and Spirit Studio. It acts as a mediator and is simply responsible for the communication.
You can install the browser extension from the Chrome Webstore.
Currently available for Chrome. Firefox, Opera and Safari will be most likely supported later on.
For paranoids (like me!): The Spirit browser extension never captures, stores or transmits data or information anywhere. It only communicates the animation data between Spirit Studio (desktop app) and the connected web page to support realtime feedback.
It might be possible that you've installed an extension that interferes with the Spirit Chrome extension. If for some reason you are unable to install the extension, please disable others and try again.
Is Spirit Studio showing a dialog that it can not load data from the web page? Then it might be possible that another extension is interrupting the communication between the web page and the Spirit Studio. Try disabling other extensions and try again.