How to correctly place commas in an English text?

The rules of punctuation in Russian and English are applied in significantly different ways. Therefore, rule number one is: do not apply Russian-language rules to texts written in English! Perhaps the most common punctuation error of Russian-speaking authors is a comma before that: “The authors demonstrate, that an increase in temperature may lead to unexpected modifications in structure".
In addition, correct punctuation in an English-language sentence can be determined by the language variant (British or American) or the chosen style of text formatting (APA, Harvard, etc.). For example, in many American English styles (APA style, for example), a serial comma is used before the last of the enumerated words (... a, b, and d). In addition, in the APA style, quotation marks are placed after the punctuation mark, not before it: “We analyzed graphs, curves, and figures.”