To use the Twilio REST API in a Delphi application, you need to sign up for a free Twilio account, purchase an SMS-capable phone number, and create an instance of the TTwilioClient class. You can then send outgoing SMS messages by posting to the Messages resource using the provided `TTwilioClient`. The code samples are written in Delphi 10.2.3 and include examples of sending a text message and making a phone call. Twilio provides a REST API reference, SDKs, helper libraries, quickstarts, and tutorials for various languages and platforms, as well as resources on sending bulk SMS messages and more.