To use Twilio SMS and Voice with a .NET 6 Minimal API, developers need to create a new project using the .NET CLI and install the required NuGet packages. They then need to configure their Twilio phone number to send HTTP requests to the server, which can be done by navigating to the Phone Numbers section in the Twilio Console and updating the webhook URL with the ngrok HTTPS Forwarding URL. The developers can then create endpoints for SMS and voice calls using TwiML or the Twilio SDK, and configure their phone number settings accordingly. Once set up, the server will receive requests from Twilio when messages are sent to the phone number or calls come in, allowing developers to respond with pre-recorded audio or text messages.