A WordPress plugin is created using a boilerplate, which provides a standard structure and files. The Nexmo PHP Library is installed via Composer, and its API is initialized in the plugin's constructor. The plugin listens to WooCommerce order status changes by hooking into the `woocommerce_order_status_` action. When an order status changes, the plugin sends an SMS notification to the customer using Nexmo's SMS API. The plugin also adds an order note with a message indicating whether the notification was successful or not.