Law enforcement officers do not have to read you your rights (also known as the Miranda warnings). Miranda applies when there is (a) an interrogation (b) by a police officer or other agent of law enforcement (c) while the suspect is in police custody (you do not have to be formally arrested to be "in custody"). Even when all these conditions are met, officers may intentionally violate the Miranda requirement. And though your rights have been violated, what you say can still be used against you. For this reason, it is better not to wait for the law enforcement officers to inform you of your rights. You know what your rights are, so you can invoke them by saying the Magic Words, "I am going to remain silent. I want to see a lawyer."
If you've been arrested and realize that you have started answering questions, don't panic. Just re-invoke your rights by saying the Magic Words again. Don't let them trick you into thinking that because you answered some of their questions, you have to answer all of them.