They're called the Miranda Rights (because they were made mandatory after the court case Miranda v. Arizona) and when an officer reads them (or recites them) to the suspect, it's called Mirandizing them. They don't actually have to be read when they are being handcuffed, they just have to be read before they are questioned or held as a suspect. But most TV shows/movies have them being read at the time of the arrest. They must be read word for word, and the suspect must acknowledge that he/she understands them.
WARNING OF RIGHTS
1. You have the right to remain silent and refuse to answer questions. Do you understand?
2. Anything you do say may be used against you in a court of law. Do you understand?
3. You have the right to consult an attorney before speaking to the police and to have an attorney present during questioning now or in the future. Do you understand?
4. If you cannot afford an attorney, one will be appointed for you before any questioning if you wish. Do you understand?
5. If you decide to answer questions now without an attorney present you will still have the right to stop answering at any time until you talk to an attorney. Do you understand?
6. Knowing and understanding your rights as I have explained them to you, are you willing to answer my questions without an attorney present?
