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We present an introduction to the chemical and computational aspects of the molecular dynamics (MD) simulation technique. Using just a few elementary ideas from classical mechanics and numerical analysis, and linear chains of identical particles as example systems, we take the reader through the steps required for the design and analysis of a simple molecular dynamics experiment. We employ the Hooke's law model for the interactions between the particles since its visualization in terms of masses and springs provides a natural model for chemical bonds. We derive the classical equations of motion in detail for the three-particle chain. We then introduce two simple methods for numerically integrating the equations of motion, one based on Euler's method for differential equations, and the other a more accurate algorithm developed by Verlet. We analyze the dynamics of the three-particle system in terms of its normal modes of vibration. Finally, exploiting the closed-form solution admitted by the Hooke's law potential, we compare the errors generated by the two integration algorithms. As supplemental material, we provide a basic MD implementation using the Euler algorithm in both Fortran and C and a set of suggested exercises.