In Postman, users can create an environment to store and reuse API credentials and other variables, allowing for easier testing of APIs. To get started, download Postman, create an account if desired, and set up the environment with Twilio's account SID, auth token, phone number, and verified non-Twilio phone number. A collection is then created to group related requests, and a new request is added to send a message using Twilio's messaging API. The request includes specifying the request type and URL, adding a request body with required variables, and sending the request. Postman also allows for testing of the endpoint by running tests in JavaScript, which can be executed automatically when the request is sent. Once the request is saved, it can be reused without having to repeat the process.