A fast leading-order Monte Carlo generator for the process $e^+e^-tomu^+mu^-gamma$ is described. In fact, using the $e^+e^-tomu^+mu^-gamma $ process as an example, we provide a pedagogical demonstration of how a Monte Carlo generator can be created from scratch. The $e^+ e^- to mu^+ mu^- gamma$ process was chosen, since in this case we are not faced with either too trivial or too difficult a task. Matrix elements are calculated using the helicity amplitude method. Monte Carlo algorithm uses the acceptance-rejection method with an appropriately chosen simplified distribution that can be generated using an efficient algorithm. We provide a detailed pedagogical exposition of both the helicity amplitude method and the Monte Carlo technique, which we hope will be useful for high energy physics students.
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