You know, just in case.
This is actually surprisingly simple. What happens is that a polygraph measures your body's level of physiological arousal (not that kind of arousal, get your mind out of the gutter!). Now, a trained spy or criminal can train themselves to feel no anxiety at all when they lie, thus no sweat or faster heartbeat or other arousal responses. A sociopath can do the same thing with no training at all, because, by their nature, it just doesn't matter to them.
But I'm going to assume you're neither spy nor sociopath, because if you were, you wouldn't need me anyway. So, when you have to take the polygraph test, take a thumbtack and hide it in your sock, so that it's not pressing into the sole of your foot, but you can bear down on it easilly. Now, when a polygraph test is administered, you'll first be asked a series of questions to center the test, a series of obvious but inconsequential questions like "Is your name John Smith?", and "Do you have brown hair?" For all of these questions, press down hard on the thumbtack with your foot when you answer. When the test begins in earnest, press the tack into your foot when you answer a question truthfully, but don't when you need to tell a lie. That's all there is to it.
Why this works: The pain which stepping on the thumbtack produces causes your body to react with the release of adrenaline and an arousal response, the same as lying would. When you step on the tack through all of the centering questions, you establish a higher baseline for yourself. When you step on the tack when you answer real questions truthfully, you conform to this baseline, and you lie without stepping on it, you're close enough to that baseline that even a skilled polygraph operator won't be able to tell the difference. Unless they notice you limping when you come in, which is more or less a dead giveaway.
Some of your more sophisticated outfits with experience administering polygraph tests know to look for this now, but with a bit more discipline, you can achieve the same affect by biting the inside of your cheek, or clenching your muscles as much as possible, though I'm told this takes some practice to pull off right.