The answer to this question used to be very straightforward. But in light of the recent Supreme Court decision of Salinas v. Texas, I’ve changed my opinion about what to do in a slight but significant way. Rather than saying absolutely nothing (which is still your second-best choice), I want people to learn to speak certain very specific words, in a firm but respectful tone, and then say nothing more.
Those words? “Officer, I assert my constitutional right to remain silent and demand to speak with an attorney.” You can click on the link to find a printable .pdf version (business-card sized) for you to keep available to yourself at all times.
You’ll hopefully never need this information, but you should have it around just in case!