Wavelet transforms (WTs) are finding increasing use in the discovery of the scale-specific properties of complex biological data. Although many efforts have been made to explain the main concepts of WT without advanced mathematics, the implicit reliance on digital signal processing terminology is widespread in many popular articles. This may cause some confusion for many biologists who do not have a clear understanding of the computational mechanisms and computer graphics of WTs. In this article we provide a tutorial on WTs for biologists by walking through two carefully selected examples step-by-step, using freely available software as well as a self-developed computer program. Both discrete WT and continuous WT are discussed, and detailed computational instructions, along with thorough interpretations of the computer outputs (or hand-calculated steps), are provided throughout. We conclude by offering a few directions for further study and several ideas on possible new developments in biological sciences using wavelets.