The prime sentence

So, this is something I teach my students, and it really helps them out, especially when they're trying to figure out the meaning of a sentence or question for their tests and what not. (I teach English as a second language for all ages in Japan, right now I'm at a JHS and about to start at SHS)

The prime sentence helps you figure out where commas have to go. You can add unnecessary commas to add pauses into the sentence; though, most conjunctions and dependent clause markers come with a pause. The same thing goes with omitted words. Necessary commas also don't come with a pause, usually.

For example, how often do you pause when you say, "Yes, I do," in response to a question? Or "Of course, I can." when someone is checking with you? The answer is you don't often pause here, but some dialects do. The pause with a comma is based on dialect, not on a specific rule.

In Japan, we use the trains to get around instead of cars.
-I don't pause for this comma, but it's necessary because the prepositional phrase is out of place.

Do your homework, and study for the test.
-I also don't pause here for two command sentences, but the comma is necessary.

I'm going to speak to your mother and discuss your attitude in class.
-No comma here, but I do pause often before this conjunction. I could add an unnecessary comma here to indicate the pause, but that makes it look/feel a bit choppy when I read through it, as if I need to pause twice.

The prime sentence is simple: Subject+verb makes up a basic sentence. Sometimes you have objects that follow, and sometimes the subject is the understood 'you' in a command sentence. Sometimes you have verb helpers like can/will, but I count those as a verb set.
-I hesitated.
-I swam ten miles.
-I can eat sushi.

Questions with question words are a bit more complicated in this realm, but leading questions are the same. Lead+subject+verb or Be-verb+subject.
-Do you like sushi?
-Can you play soccer?
-Are you here?
-Is John a football fan?

With question words, as I said, it's a bit more complicated. Question word+topic+lead+subject+verb or question word+topic+be-verb+subject.
-What sport do you like?
-Where can I eat the best sushi?
-What time is it?
-Who is that? (This one combines the question word and the topic)

Finding the prime sentence will make sure you never miss necessary commas/semicolons.

I like sushi, and I went swimming.
-'I like sushi' is a prime sentence.
-'I went swimming' is a prime sentence.
-Thus, when combining the two with a standard conjunction, you need a comma.
-Dependent clause conjunctions don't require the comma (I like sushi when I go swimming), but you must make sure the tense of both verbs match when you combine them with a dependent clause conjunction.

I'll probably go deeper into this later on with unnecessary commas and the pause later, but I hope this gives you something to think about when constructing your sentences to help reduce basic punctuation errors)