Trying to detect whether a person is telling a lie or telling the truth by watching the eye movement is a highly publicized technique, often used in police interrogations and job interviews. The validity and efficiency of the method is, however, not 100% fool-proof, because there may be other reasons or even medical conditions which cause the eyes to move.
Here is the theory: construction mode (lying) and memory mode (remembering facts) are located in the opposite sides of the brain. Which side depends on the individual, among other things, whether they are right handed or left handed. When telling a lie, the eyes will automatically swivel to the construction mode side of the brain and vice versa. It needs keen observation and practice to find out which is which, that's why often questions like: what's your date of birth? or what did you have for lunch? are asked first, because it can be assumed that a person has no reason to lie about these facts. Once it has been established which side the memory mode is located in, tricky questions which might call for a lie, will follow.
Making constant eye contact is also often construed as a sign for telling the truth, but that kind of behavior can be trained and in some Asian cultures staring constantly at a person is considered impolite. Repeated eye blinking can indicate a lie, but the condition can have other causes as well.
Another body signal which indicates a lie is touching the ear, neck or mouth, an atavistic behavior which is thought to originate the legend of the Three Apes - see nothing, hear nothing, say nothing. Fiddling hands, rubbing palms along the leg, frequently crossing and re-crossing the legs all indicate nervousness, which may be caused by telling a lie. All these parts of body language need to be interpreted in conjunction with the spoken word, although it's also said that involuntary body language is the much more reliable part of a conversation.