One standard use for commas is to separate elements in a series.
Example : "I brought a pen, a notebook, and a ruler to class."
I believe the Oxford comma is necessary. I almost always use it. If I don't...well, I think of this cartoon.
I turn to the Oxford comma for clarity.
Another standard use for commas is to separate independent clauses. You can use commas to separate independent clauses that are joined by "and", "but", "for", "or", "nor", "so", and "yet".
Example: My father is very kind, and I have learned a lot from him.
An independent clause is a sentence that can stand on its own. To test this out, you need to see if the second part of the sentence would be a full sentence on its own after the removal of the comma and "and". This example works, and this is an example of using a comma to separate independent clauses.
Another standard use for commas is to separate an introductory word or phrase.
Example: However, I don't think this is true.
Commas can get tricky. Sometimes they are put in places where they do not belong. This can cause confusion. I found a couple of sentence examples where a comma is used incorrectly. At first glance, I would not think that the following sentence was incorrect.
Lisa waved at Nancy, laughing joyously.
When I first looked at this sentence, I thought it was correct. Then I read the question next to the sentence: Who is laughing, Lisa or Nancy?
WELL, good question. Who IS laughing? I am assuming that it is Lisa, but the sentence isn't clear. The following would be a much more appropriate way of wording the sentence.
Laughing joyously, Lisa waved at Nancy.
It makes sense to me now, but this probably would have been a mistake I would make in my writing.
A good general tip I found is to use commas whenever necessary to prevent confusion or misreading. While you do not want to put unnecessary breaks and pauses into a sentence, you want to make sure that you are conveying what you want to say in a clear way.
I mean, we have all seen these ecards floating around on Facebook and Pinterest.
And goodness knows I don't want to eat my dog.
References
https://owl.english.purdue.edu/owl/owlprint/607/