Police officers don't have to provide the Miranda warning to people they arrest. They're free to arrest you, put you in the back of a patrol car, and take you to the station for booking without once mentioning your rights.
The Miranda rights are relevant only when a suspect is:
If the police had you in custody and questioned you about the alleged crime without providing the warning, the prosecution typically wouldn't be able to use your resulting statements at trial. (Of course, there are exceptions to the Miranda rule, and statements obtained in violation of Miranda are generally admissible to impeach a defendant who testifies.) But if the police never interrogate you, then they don't have to read you your rights—if you speak up of your own accord, what you say may very well be admissible.
For all kinds of information about the Miranda rights, see Police Questioning of Suspects: The Miranda Rule.