One thing people need to be aware of is state laws on the right to STFU differ. In MA once you express your desire to take the 5th or have counsel, questioning must stop. The police are not allowed to proceed to convince you to change your mind, or play the "just be silent then, we'll show you what we have, then you can think over your decision". Of the tricks that sexual assault investigator told me that he said almost always works - "Sure, you can have an attorney present but the first thing she/he/it will say is to not answer any questions, and you will lose your opportunity to tell me your side of the story".
If a suspect is represented by counsel for an outstanding charge, the suspect cannot waive his right to remain silent in MA and may not be questioned until that counsel is brought into the loop. Other states are not as protective of suspect's rights.
Persons must not only know how to invoke the right to remain silent, but also be aware the police in some states may legally engage in mind games after you have invoked that right to try to convince you to change your mind.