When an officer places you under arrest, he or she will tell you about your rights. These include the right to remain silent.
It is imperative to understand the importance of this right as many people get themselves into more trouble or cause issues for their defense by talking too much when in custody. The general rule is that you have the right not to talk to officers, but the ACLU explains there are a couple of points to keep in mind.
You have the right not to answer questions that officers ask you. You should provide your name if asked, but that is the extent of what you need to say. Officers will likely continue to ask you questions and try to get you to talk, which is their right. But you can simply respond that you choose to extend your 5th amendment right. There is nothing an officer can do when you choose to exert your rights to compel you to talk without it being a violation.
You may have to keep repeating that you choose to remain silent. Officers often count on being able to wear you down to get you to start talking. It is in your best interest, though, to not say anything to anyone except your attorney.
There is one exception to your right to remain silent. Staying silent means you do not talk. It does not mean you can supply inaccurate information. It is illegal to lie to a law enforcement officer. If you do so, you could face additional charges. If you think about lying, remember it is better to just stay quiet.
In general, when you land in police custody, you should stop talking. Only offer your name, and refuse to answer any other questions by evoking your rights.