Z-scores are used to standardize data by converting it to a scale where the mean is 0 and standard deviation is 1. This allows for comparison of different variables measured on different scales. To calculate a z-score, the individual value, population mean, and population standard deviation are input into the z-score formula. Z-scores can be used to find the probability that a data point falls at or below a certain value based on its distance from the mean in terms of standard deviations using the normal distribution and z-score tables.