Law enforcement officials are required to read any suspect in their custody their Miranda rights prior to interrogating them. Some of the most important protections that officers are required to let a suspect know they have is to have an attorney present and to remain silent.
Once a suspect invokes his or her right to remain silent or to have an attorney accompany him or her during an interrogation, law enforcement is required to honor the requests and discontinue questioning of him or her. If they don't or a suspect is never read his or her rights, then prosecutors may be prohibited from using any information he or she provides thereafter at trial.
If a suspect chooses to waive his or her rights then he or she must either write a statement to that effect or otherwise verbalize those sentiments. It is possible for police to obtain what's referred to as an "implied waiver". In this case, so long as law enforcement state and verify that the suspect understands his or her rights, certain behavioral traits he or she may engage in may be taken as a waiver of them.
One example of an implied waiver is if a suspect is advised of his or her rights, sits silent for a while, then begins sharing self-incriminating information about his or her alleged involvement in criminal activity.
It's also important to know that waivers of Miranda rights aren't intended to last forever. Instead, a suspect who initially decides to speak to interrogators can later decide to invoke his or her Miranda rights if he or she chooses. Once he or she does, only the information that he or she shared prior to invoking his or her rights will be admissable in the court of law.
If you're being investigated for having committed a crime, then it's important that you speak with a New York criminal defense attorney prior to making any statements to police to ensure that you don't jeopardize your case.
Source: FindLaw, "Waiving Miranda Rights," accessed June 01, 2018