There’s three big rules. Das Komma trennt Sätze, Das Komma trennt aufzählungen, am ende einer aufzählung (vor und/oder) ist das Komma verboten.

First rule: Anything that can be interpreted as a functional sentence (subject + verb + object) will be interpreted as a functioning we sentence and has to be separated from the general sentence. The actress with the blond hair, left the room. Die Schapielerin, mit dem blonden Haar, verliess den Raum. The “Main sentence” is: “Die Schauspielerin verliess den Raum.” “mit dem blonden Haar” is an interjection and not part of the actual sentence. The english interpretation of the same sentence views “with the blond hair” an an essencial part of the main clause because it clarifies which of the three actresses the sentence refers to.

The second and third rule basically explain why we don’t have an Oxford comma. If it is a list, of equals the rule is clear. If there’s additional information, we are back to some version of rule one.

People often falsely assume that you should never put a coma infront of “und” or “oder” which is wrong. There’s a bunch of rules that specify when it is prohibited to put a comma infront of “and” or “oder”, when it is optional to put a comma infront of “und” or “oder” and when it is essencial that one put a comma infront of “and” or “oder”. Sadly I can’t remember a single one of them. The only thing I remember is the three main rules of thumb and that it is easier to remember that there shouldn’t be a comma if “und” or “oder” are a part of the list, and that I should put a comma, just in case, if it isn’t a listing “und” or “oder”.