If the distribution is uncertain, the data can be plotted as a normal probability plot and visually inspected, or tested for normality using one of a number of goodness of fit tests, such as the Kolmogorov–Smirnov test.
One thing I want to clarify is the assumption of normality when using parametric tests like the two-sample t-test. The article mentions using tests like Kolmogorov–Smirnov or Shapiro–Wilk, but it also says large samples (n > 30 or even 100) can approximate normality. This makes me wonder how strict researchers need to be in practice. If a dataset is slightly skewed but has a large sample size, is it still appropriate to proceed with a t-test? It seems like there is a balance between theory and practical application that isn’t always clearly defined.