The one simple thing is: there are no rules in English. In German you 'have to' use a comma after this or that word. There are no such rules in English. Put them where you want them - where your voice falls and rises, is a good idea. That covers most of the conventional uses. We have places where we often use them, and you can learn those by experience, but it is not that important. People will disagree, and there are no right answers.
Ok, same as in French, then
Your answer suits me: I just wanted to know if there were "extra rules" I didn't know.
PS: when you say it's not important, I think of some French "counter-example" that seems to work in English too: saying "We are about to eat, the children say." or "We are going to eat the children, say" seems very different to me (but maybe my sentences are incorrect grammatically?).
Oh of course you have to use commas - and their placing can make a big difference. I'm not saying ignore them completely. But use them as you see fit. There are strict rules in, say, German - you must use a comma before dass regardless of how you pronounce it or what it means. In English, fit them to your meaning. Use it if it helps shape the meaning, or if it helps guide the pronunciation. There are some conventions (e.g. 'a tall, dark stranger': two equal adjectives before a noun), but you can ignore them if they don't fit what you want to say or how you say it.