How do you calculate the p-value in a hypothesis test?

Answer 1

For a given distribution, the p-value is the probability of getting a test statistic greater than the one you calculated. As an example, suppose your test statistic for a normal distribution is Z=1.96 For a two sided test then add the probabilities for Z<-1.96 and Z>1.96.

The p-value depends on whether you're doing a one sided or two sided test.

Answer 2

You calculate it using a calculator with statistical features or look it up on a table.

The actual calculation is a calculus integral of a function that is defined according to the type of distribution you're using. For a z-test, the function is a transformation of e^(x^2).