What are the standard tests for determining the logical validity of syllogisms?

Question

As an exercise, I would like to write a simple program which will take as inputs three propositions (AEIO) and output true or false based on if the resulting syllogism is valid or not. Obviously, I need a rigorous understanding of exactly when a syllogism is valid. The Wikipedia article (https://en.wikipedia.org/wiki/Syllogism) mentions 256 possible syllogisms out of which 24 are valid. That opens the possibility of a hard-coded table. The following article (http://www.uky.edu/~rosdatte/phi120/lesson17a.htm) speaks of the "rule method" for determining validity but I am unclear if these are merely necessary or sufficient conditions. My question is this: what are the standard tests for syllogism validity? I would ideally like several different options to get a sense of what options are available and which are best for a computer based on different trade-offs.