Commas

We use commas to prevent possible confusion or misreading, i.e. for semantic reasons, but they have essential syntactical functions too:

1. to separate independent clauses (those with a subject and a predicate [a verb with or without a complement]) when they are joined by the coordinating conjunctions and, but, for, or, nor, so, yet [the F-A-N-B-O-Y-S] (but not necessarily before and, but, or or when the clauses are short, and not when the and links two verbs [a compound predicate] rather than two clauses)

   The minutes would pass, and then Einstein would stop pacing as his face relaxed into a gentle smile. [N.B. Most people, according to my mother, skip cleaning in the corners; but, she used to say, they don't skip payday.]
   

2. after introductory clauses (e.g. beginning with after, although, as, because, if, since, when, while), phrases (i.e. participial and infinitive phrases, absolute phrases, nonessential appositive phrases and long prepositional phrases) or words (e.g. however [transitional expressions], well [interjections], yes or no) [except when the clause or phrase is short and omitting the comma doesn't cause confusion. N.B. 1. Commas are not used after phrases that introduce inverted sentences. N.B. 2. A clause has a finite verb; a phrase does not—though it may have a verbal.]
   

   When you write, you make a sound in the reader's head.
   

3. to set off non-essential clauses, phrases and words (e.g. modifiers, appositives, absolute phrases [a part of a sentence not grammatically connected to anything else]), contrasted elements, parenthetical expressions, interjections

   Some people lie, as my grandmother observed, because they don't know how to tell the truth. The ringed planet, Saturn, can be seen at dawn. His temper being what it is, I don't want a confrontation. Human beings, unlike oysters, frequently reveal their emotions. Language, then, sets the tone of our society. Now is the time, my friend, to stop smoking.
   

4. to separate three or more parallel words, phrases or clauses written in a series, including co-ordinate adjectives
   
5. to set off all geographical names, items in dates (except the month and day), addresses (except the street number and name), and titles in names
6. to shift between the main discourse and a quotation