A common misconception that people often have is that the police are always required to read you your Miranda rights any time they stop you. This is not entirely correct. The police are only required to read you your Miranda warnings if you are the subject of what is known as a custodial interrogation. What is or is not a custodial interrogation is a question of law. The courts have held that certain types of questions such as your name and where you are going are not custodial care occasions.
According to the American Civil Liberties Union, what you do need to remember when dealing with the police is that you always have the right to remain silent. You are required to identify yourself when asked by a police officer, but nothing further. If the police ask for permission to search you, your home or any vehicle that you have to be in, you should always refuse. They may still have a legal basis for searching anyway, but you should never voluntarily give up any of your constitutional rights. If the police continue to try and question, you need to tell them you will answer no questions without your attorney present.
There are many cases where the only real evidence the prosecution has against suspects is statements made to the police in response to questioning. Even if you have made a statement to the police, that does not necessarily mean the police can use that statement against you. There are precise evidentiary rules that cover when that statement can appear as evidence in a trial. If the report was the product of threats, force or coercion, that statement might not be admissible.