If I’m arrested, do the police have to “read me my rights”?

No. However, if they start questioning you but haven’t read you your rights, they can’t use anything you say as direct evidence against you at trial. What are these rights? Popularly known as the Miranda warning (ordered by the U.S. Supreme Court in Miranda v. Arizona), your rights consist of the familiar litany invoked by TV police immediately upon arresting a suspect:

It doesn’t matter whether an interrogation occurs in a jail or at the scene of a crime, on a busy downtown street, or in the middle of an open field: If you are in custody (deprived of your freedom of action in any significant way), the police must give a Miranda warning if they want to question you and use your answers as direct evidence at trial. If you are not in police custody, however, no Miranda warning is required. This exception most often comes up when the police stop someone on the street for questioning about a recent crime and the person blurts out a confession before the police have an opportunity to deliver the warning.

Read more at http://www.nolo.com