Inaccurate measurements occur regularly in data acquisition as a result of improper sampling times. An understanding of proper sampling times when collecting data with an analogue-to-digital converter or video camera is crucial in order to avoid anomalies. A proper choice of sampling times should be based on the Nyquist sampling theorem. If the sampling time is chosen judiciously, then it is possible to accurately determine the frequency of a signal varying periodically with time. This paper is of educational value as it presents the principles of sampling during data acquisition. The concept of the Nyquist sampling theorem is usually introduced very briefly in the literature, with very little practical examples to grasp its importance during data acquisitions. Through a series of carefully chosen examples, we attempt to present data sampling from the elementary conceptual idea and try to lead the reader naturally to the Nyquist sampling theorem so we may more clearly understand why a signal can be interpreted incorrectly during a data acquisition procedure in the case of under sampling.