Much of the advice here is good, but some is a bit weird.
> I will give the document to my brother, Tom. (The writer has only one brother. The brother's name is nonessential and therefore set off with a comma.)
> I will give the document to my brother Tom. (The writer has more than one brother. In this case, the specific brother—Tom—is essential information and should not be set off with a comma.)
I know this used to be considered an important distinction, but I think few writers would worry about it today. Does the reader care if Tom is the writer's only brother? Either way the writer is talking only about Tom, not any possible other brothers. I think many writers today would leave out the comma in either case.
Take an example where it's clear there is only one:
I am going to visit my mother Helen.
I am going to visit my mother, Helen.
I don't think leaving out the comma implies that I have more than one mother, and I doubt if anyone cares much about the comma here either.
The trend today is to simply leave out commas where the meaning is clear.
This example of the Oxford comma is really confusing:
> I am taking art history, Russian literature, microeconomics, and macroeconomics next semester.
It's a valid point that omitting the Oxford comma could make it sound like "microeconomics and macroeconomics" is a single course, but using the comma makes it sound like the first three courses are being taken this semester and macroeconomics next semester. It should be rewritten:
> Next semester I am taking art history, Russian literature, microeconomics, and macroeconomics.
There is a similar situation where the Oxford comma is needed in the programming joke:
There are two hard problems in computer science: naming things, cache invalidation, and off-by-one errors.
It ruins the joke (to my eyes) if you leave it out:
There are two hard problems in computer science: naming things, cache invalidation and off-by-one errors.
And enough with the commas already in a sentence like this:
> Your work has been, frankly, awful.
Ugh. Does anyone actually write that instead of:
Your work has been frankly awful.
(Of course I would never say that to someone but would find a more constructive way to put it.)
My advice: Write simply and clearly. Know these purported rules but take them with a healthy grain of salt. Omit unnecessary punctuation where the meaning is clear to the reader. And if you need extra punctuation to avoid confusion, consider rewriting the sentence for clarity.