Setting off introductory clauses with commas helps the reader identify the subject of the sentence. If you add an introductory clause or word, you must set it off with a comma.

(Ex.) Having five children my mother sacrificed a lot . (Incorrect)

Having five children , my mother sacrificed a lot . (Correct)

Without the comma in the previous example, the reader may read the sentence as one introductory clause (and wonder why the mother was sacrificing children). With the comma, however, it is clear that my mother is the subject of the sentence and she has five children.

Where the commas go in the sentence depend on whether the introductory phrase is a clause or a word.

(Ex.) Although I am allergic to peanuts , I eat them all the time . (Correct: after introductory phrase)

However , they make me itch . (Correct: after introductory word)

However many I eat , I still want more . (Correct: after introductory phrase)

In each of the previous examples, the comma comes just before the subject of the sentence.

If you are adding nonessential information to an already complete sentence, you must set it apart with commas.

(Ex.) Dr. Soandso my professor is at the beach this week. (Incorrect)

Dr. Soandso , my professor , is at the beach this week . (Correct)

My professor is nonessential information. You may remove it without changing the meaning of the sentence.

Restrictive elements are those which are necessary to the meaning of the sentences. Do NOT set off restrictive information because it may affect the meaning of the sentence

(Ex) Students, who arrived late, lost five points . (Incorrect)

Students who arrived late lost five points. (Correct)

Since only students who arrive late lost five points, the phrase who arrive late is restrictive elements. It should not be set off in commas.

(Ex) Those students, who are majoring in biology, are reviewing for their test. (Correct)

In this example, the information who are majoring in biology is not necessary, thus it is not restrictive and should be set off in commas.

(Ex.) Shakespeare's play , "Hamlet , " is very long. (Incorrect)

Shakespeare's play "Hamlet" is very long . (Correct)

Because Shakespeare wrote more than one play, the first sentence is incorrect. Hamlet is not Shakespeare's only play. The sentence Shakespeare's play is very long is not clear by itself because we don't know which one of Shakespeare's plays after very long.

To see if your modifier needs commas, drop the modifier and see if the sentence still makes sense.

(Ex.) Doctors , who have busy schedules , are stressed . (Incorrect)

Doctors are stressed . (Correct, but not what I was trying to say)

Doctors who have busy schedules are stressed . (Correct)

If you remove the clause in between the commas, the meaning of the sentence is altered. All doctors are not necessarily stressed, so "who have busy schedules" is required to make it make sense. If the clause is required in the sentence, no commas are needed.

Sometimes it's unclear if you should start a clause with that or which. That should be used when a clause in essential to the sentence's meaning. Which should be used when you are adding nonessential information.

(Ex.) Houses that have a lot of windows are hard to keep clean . (Correct)

My house , which has a lot of windows , is yellow . (Correct)

In the first sentence, the clause with that gives essential information and does not need to be set apart by commas. The houses are hard to keep clean because they have a lot of windows. In the second sentence, the clause beginning with which adds more information to the sentence but is nonessential, therefore it needs to be separated with commas. The phrase simply tells the reader an extra detail about the house. If that was used (and the phrase was not set off in commas), it would imply the writer has numerous houses, but the yellow one has a lot of windows. Thus, that and which can alter the meaning of the sentence.