How may one properly invoke the right to silence?

If you want to invoke your right to remain silent, you must do two things: First, you have to make it known that you are invoking your right to remain silent. In other words, the best way to make sure your right to silence is honored is to explicitly say something like, "I am invoking my right to remain silent." The second thing you must do is actually shut up and remain quiet. You're not allowed to selectively choose to be quiet about some things, while opting to talk about others.

Once someone has effectively invoked their right to remain silent, police have to back off and honor that right. They can't keep badgering the detainee with questions trying to get them to change their mind. Note, however, this doesn't mean they can't ever ask the detainee questions until the end of time. After a while (e.g., weeks later) police can re-Mirandize the detainee and ask them questions so long as those questions are about a crime that is unrelated to the one the person originally invoked their right to remain silence for.