I'm obsessed with interrogations, and have watched several hundred hours of them. It's interesting to see how many cops use the same techniques to get suspects to talk, and it almost always works.
The way to win is not to play.
As soon as it's clear you will be asked questions, immediately say, "I am invoking my right to refuse to answer any questions, and I will not answer any questions unless and until I can consult with an attorney."
And then don't let them trick you into changing your mind, because they will. They'll say, "Oh, I can't talk to you and answer your questions because you invoked your rights." It's a bullshit ploy to get you to rescind your invocation. They don't have anything to say that you need to hear.
The next thing you should say after invoking is, "Am I free to leave?" Because unless you're being legally detained, they must answer this question truthfully. If you are free to leave, get up immediately and leave. If you're not free to leave, "Keep your mouth shut, put your head down, and take a nap. If they say you can leave if you help then with a few questions, tell them to pound sand and get you a lawyer.
Talking to them, answering their questions, or agreeing to a polygraph will all get you locked up. Never take the poly, under any circumstances, even if you have nothing to hide. That test can only hurt you. It will never help you despite what they say. Don't do it.
Do all this, and you'll be back home in no time. Be strong, and don't make the mistake of thinking that honesty and cooperation will set you free, because it won't.