First you have to install the JSON API for WordPress Plugin.
To install JSON API for BuddyPress just follow these steps:
- upload the folder "json-api-for-buddypress" to your WordPress plugin folder (/wp-content/plugins)
- activate the plugin through the 'Plugins' menu in WordPress or by using the link provided by the plugin installer
- activate the controller through the JSON API menu found in the WordPress admin center (Settings -> JSON API)