Determine if your sample size is too small enough to run non-parametric tests. As a general rule of thumb, a sample size of under 100 is considered "small" by most standards. The three major non-parametric tests are Kolmogorov-Smirnov, Wilcoxon matched pairs test and the Sign test.
Choose a non-parametric test to run on your data. Choose the Kolmogorov-Smirnov test if you want to detect differences between means. Choose the Wilcoxon matched pairs test if you want to rank differences in observations. Otherwise, choose the Sign test,
Determine the importance of the study you are undertaking. An important study would be one that might risk life or health (for example, you're studying the efficacy of a new drug). If the results of your study are important, run all three non-parametric methods and compare the results.
Run one of the tests on your data by graphing a relevant distribution and rejecting or accepting the null hypothesis.