To calculate the z-test, the mean is subtracted from each observation, and then this difference is by the standard deviation.
An example of the z-value is to find the area under the distribution of P(0 to z) when z = 1.96. To calculate this area, a table of the area under the normal curve is used. The z score is found first by taking the first part of the z score (1.9) and find this value under the first column. Then the second decimal place (or.06 of the 1.96) is found on the top row. The intersection of this column and row gives the total area under the bell shaped curve. This is the probability that this event will take place.
Lind, D., Marchal, W., & Wathen, S. (2011). Basic statistics for business and economics (7th ed.). New York, NY:McGraw-Hill/Irwin.