The police will often read these rights off a preprinted card. They will read you these rights only if they intend to question you. After reading them to you, they will question you in an effort to get you to incriminate yourself. They will write down your statements, and often ask you to sign a written version. Answering questions but refusing to sign a written statement doesn't help you.
Oral confessions can be just as damaging as signed written ones.
Answer no questions until you have spoken with a lawyer. It could result in a major blow to the case against you. Even a full written confession to the crime can be thrown out of court. However, although evidence is thrown out, remember that the case itself is not necessarily dismissed. If there is other evidence of your guilt, that other evidence could still be used to prosecute you.