All requests to sensitive areas of the Twilio API must use HTTP Basic Authentication. Authenticate using your Account SID as the username, and your Auth Token as the password. Both can be found in the Twilio Console.
You can also generate revocable API Keys to authenticate.
You may want to consider using a Twilio helper library (available in PHP, .NET, Java, Ruby, Python and Node.js) as they will take care of authentication for you.