This depends on the data set. Thorough research data in a pandas DataFrame,1-D NumPy array or NumPy multi-array will make some difference in which technique(s) to use. And whether you use code or not.
What we did in class was done to show the math behind the coding. Z-score was taught, variables were set/known and it was used to show one of the techniques. There is also Manhattan, Euclidean, Max-min when standard deviation and mean are unknown.
Remember the purpose of Standardization and Normalization, they are there to scale for visualization (graphing). These new points/coordinates will be different than graphing the original points in the data set.
If you are coding, depending on your preference on libraries, most likely there are two lines of algorithms to find normalization and standardization. The norm function is usually the first and the transformation is done second.
This is a code I wrote, it is using just NumPy to perform Manhattan Normalization.