To build a Twilio-hosted group messaging service with sync, functions, and SMS, one can use Twilio's services to manage their own group SMS application. This allows users to communicate quickly and effectively with friends, colleagues, or customers using an SMS app on any mobile phone. The implementation is managed using the Twilio Console, with no developer skills required, and involves creating a Twilio Function, Messaging Service, Notify service, and Sync service to manage the member list. Testing the application involves sending messages to the group phone number and testing user subscriptions and broadcasts. The configuration steps are detailed in the Owl Group SMS GitHub repository, and the implementation can be expanded to create multiple groups using separate Twilio phone numbers and services.