What is the phrase that the police use when taking somebody into custody?

Answer 1

"You do not have to say anything, but it may harm your defence if you do not mention when questioned something which you later rely on in court. Anything you do say may be given in evidence."

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Slightly different version in the US- known as the Miranda Rights or Miranda warning- and it DOES vary slightly from state to state:

"You have the right to remain silent. Anything you say can and will be used against you in a court of law. You have the right to speak to an attorney. If you cannot afford an attorney, one will be appointed for you. Do you understand these rights as they have been read to you?"

Added: In the US, it is uncommon for officers to read Miranda immediately upon arrest. Miranda warnings protect defendants from interrogation. Therefore, Miranda is most commonly read after the arrest, before an interrogation.