1. Use a comma to separate the elements in a series (three or more things), including the last two. "He hit the ball, dropped the bat, and ran to first base." You may have learned that the comma before the "and" is unnecessary, which is fine if you're in control of things. However, there are situations when, if you don't use this comma (especially when the list is complex or lengthy), these last two items in the list will try to glom together (like macaroni and cheese). Using a comma between all the items in a series, including the last two avoids this problem.
2. Use a comma + a little conjunction (and, but, for, nor, yet, or, so) to connect two independent clauses, as in "He hit the ball well, but he ran toward third base."
3. Use a comma to set off introductory elements, as in "Running toward third base, he suddenly realized how stupid he looked."
4. Use a comma to set off parenthetical elements, as in "The Founders Bridge, which spans the Connecticut River, is falling down." By "parenthetical element," we mean a part of the sentence which can be removed from a sentence without changing the essential meaning of that sentence. The parenthetical element is sometimes called "added information." This is the most difficult rule in punctuation because it is sometimes unclear what is "added" or "parenthetical" and what is essential to the meaning of a sentence.
5. Use a comma to separate coordinate adjectives. You could think of this as "That tall, distinguished, good looking fellow" rule (as opposed to "the little old lady") If you can put an and or a but between the adjectives, a comma will probably belong there. For instance, you could say, "He is a tall and distinguished fellow" or "I live in a very old and run-down house." So you would write, "He is a tall, distinguished man" and "I live in a very old, run-down house." But you would probably not say, "She is a little and old lady," or "I live in a little and purple house," so commas would not appear between little and old or between little and purple.
6. Use a comma to avoid confusion (your professor's escape rule).
7. Darling's Famous Rule of Punctuation: Never use only one comma between a subject and its verb. "Believing completely in oneself [no comma here, even though one might well pause]is essential for success."