Restrictive or Essential Adjective Phrases
The newspapers \in the attic are garbage. The newspapers \in the den are not garbage.Without the phrase, I might throw out the wrong newspapers.
My father, \with his fear of crowds, did not come with us to the state fair.I don't need to know about his fear of crowds to know which father I am talking about.
Commas with Adverb Phrases
Adverb phrases at the beginning of the sentence, now introductory prepositional phrases, are usually separated from the sentence by a comma unless they are very short (three words or fewer) and it is easy to tell where the phrase ends.
In the morning we got up and got ready for work.
In the morning, we got up and got ready for work.
(Short phrase okay with or without a comma.)
This is one of the few places where how a sentence sounds determines the punctuation.
Without my work, I was tempted to skip class.
(Short, but pauses. It is obvious that work does not describe I.)
Prepositional phrases layered together usually have a comma.
On the morning before my birthday, my parents surprised me with a trip to Hawaii.
Commas are especially important if the object of the preposition is a verb acting like a noun. Otherwise, the results can be funny.
After vacuuming my brother collapsed on the couch. (Was someone vacuuming your brother?)
After vacuuming, my brother collapsed on the couch. (Comma is necessary)
Sometimes for effect, writers turn the whole sentence around, using the prepositional phrase first, then the verb, and finally the subject.
Down the stream paddled the kayakers.
This is not an example of an introductory phrase and does not need a comma.