In the United States, periods and commas go inside quotation marks regardless of logic.
 

 Further punctuation around quoted speech or phrases depends on how it fits into
 the rest of your text.

When an attribution of speech comes in the middle of quoted language, set it apart as you
 would any parenthetical element:

"I don't care," she said, "what you think about it."

 Be careful, though, to begin a new sentence after the attribution if sense calls for it:
"I don't care," she said. "What do you think?"

 Convention normally insists that a new paragraph begins with each change of speaker:
 "I don't care what you think anymore," she said, jauntily tossing back her hair and looking askance at Edward.  "What do you mean?" he replied.  "What do you mean, 'What do I mean?'" Alberta sniffed. She was becoming impatient and wished that she were elsewhere.  "You know darn well what I mean!" Edward huffed.  "Have it your way," Alberta added, "if that's how you feel."

 In reporting "silent speech"—noting that language is "said," but internally and not spoken out
 loud—writers are on their own. Writers can put quotation marks around it or not:
Oh, what a beautiful morning, Curly said to himself.  "Oh, what a beautiful morning!" Curly said to himself.

 Be careful not to use quotation marks in an attempt to emphasize a word (the kind of thing
 you see in grocery store windows—Big "Sale" Today!). Underline or italicize that word
 instead. (The quotation marks will suggest to some people that you are using that word in a
 special or peculiar way and that you really mean something else—or that your sale is entirely
 bogus.

When two ideas come together and either one of them can stand by itself, as its own, independent sentence, the following kinds of punctuation are possible. (Review, also, the sections on Coherence: Transitions Between Ideas and on avoiding Run-on Sentences.)

 1) Period + start a new sentence
 
My grandmother refuses to go to bed early. She thinks she's going to miss out on  some of the action.
 
2)  Comma + a cute little conjunction (and, but, for, nor, yet, or, so)
 
My grandmother refuses to go to bed early, and I'm afraid she's going to catch a  bad cold.

 3) Semicolon by itself. Where you have used a semicolon, you could have used  a period, but the semicolon, you felt, is better (probably because the independent  clauses are so closely related and nicely balanced).

 In spite of her cold, my mother refuses to go to bed early; she is afraid she will  miss something.
 
4) Semicolon + big ugly conjunction or other transitional expression  (however, moreover, nevertheless, therefore, as a result, consequently . . . )  followed by a comma.
 My mother has stayed up late four nights in a row; as a result, she cannot seem to  get well.

    A SENTENCE FRAGMENT fails to be a sentence in the sense that it cannot stand by itself. It does not contain even one independent clause. There are several reasons why a group of words may seem to act like a sentence but not have the wherewithal to make it as a complete thought.
 

  It may locate something in time and place with a prepositional phrase or a series of such phrases, but it's still lacking a proper subject-verb relationship within an independent clause: In Japan, during the last war and just before the armistice. accomplishes a great deal in terms of placing the reader in time and place, but there is no subject, no verb.
 

      It describes something, but there is no subject-verb relationship: Working far into the night in an effort to salvage her little boat. This is a verbal phrase that wants to modify something, the real subject of the sentence (about to come up), probably the she who was working so hard.
 

      It may have most of the makings of a sentence but still be missing an important part of a verb string: Some of the students working in Professor Espinoza's laboratory last semester

 Remember that an -ing verb form without an auxiliary form to accompany it can never be a verb.

 It may even have a subject-verb relationship, but it has been subordinated to another idea by a dependent word and so cannot stand by itself: Even though he had the better arguments and was by far the more powerful speaker. This sentence fragment has a subject, he, and two verbs, had and was, but it cannot stand by itself because of the dependent word (subordinating conjunction) even though. We need an independent clause to follow up this dependent clause: . . . the more powerful speaker, he lost the case because he didn't understand the jury. 

A RUN-ON SENTENCE has at least two parts, either one of which can stand by itself (in other words, two independent clauses), but the two parts have been smooshed together instead of being properly connected. Review, also, the section which describes Things That Can Happen Between Two Independent Clauses.
It is important to realize that the length of a sentence really has nothing to do with whether a sentence is a run-on or not; being a run-on is a structural flaw that can plague even a very short sentence: The sun is high, put on some sun-block

 An extremely long sentence, on the other hand, might be a "run-off-at-the-mouth" sentence, but it can be otherwise sound, structurally. Click here to see a 239-word sentence that is a perfectly fine sentence (structurally).  When two independent clauses are connected by only a comma, they constitute a run-on sentence that is called a comma-splice. The example just above (about the sun-block) is a comma-splice. When you use a comma to connect two independent clauses, it must be accompanied by a little conjunction (and, but, for, nor, yet, or, so). The sun is high, so put on some sun-screen.
 

Run-on sentences happen typically under the following circumstances:

 a.When an independent clause gives an order or  directive based on what was said in the prior  independent clause:  This next chapter has a lot of difficult information in it, you should start studying right away
 (We could put a period where that comma is and start a new  sentence. A semicolon might also work there.)

b.When two independent clauses are connected by a  transitional expression (conjunctive adverb) such  as however, moreover, nevertheless.  Mr. Nguyen has sent his four children to ivy-league colleges, however, he has sacrificed his health working day and night in that dusty bakery
 (Again, where that first comma appears, we could have used  either a period -- and started a new sentence -- or a  semicolon.)

c.When the second of two independent clauses  contains a pronoun that connects it to the first  independent clause. This computer doesn't make sense to me, it came without a manual. (Although these two clauses are quite brief, and the ideas are  closely related, this is a run-on sentence. We need a period  where that comma now stands.)  Most of those computers in the Learning Assistance Center are broken already, this proves my point about American computer manufacturers. Again, two nicely related clauses, incorrectly connected -- a  run-on. Use a period to cure this sentence.

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.

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."

Contending that the coordinating conjunction is adequate separation,
 some writers will leave out the comma in a sentence with short, balanced
 independent clauses (such as we see in the example just given). If there is ever any
 doubt, however, use the comma, as it is always correct in this situation.

 One of the most frequent errors in comma usage is the placement of a comma after a
 coordinating conjunction. We cannot say that the comma will always come before the
 conjunction and never after, but it would be a rare event, indeed, that we need to follow a
 coordinating conjunction with a comma. When speaking, we do sometimes pause after the
 little conjunction, but there is seldom a good reason to put a comma there.

 See the note below regarding the use of a comma between two independent clauses when the
 second independent clause begins with a parenthetical element or adverbial clause.

Use a comma to set off introductory elements, as in "Running toward third base, he suddenly realized how stupid he looked."

It is permissible to omit the comma after a brief introductory element if the omission does not result in Confusion or hesitancy in reading. If there is ever any
 doubt, use the comma, as it is always correct.

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 a sentence which can be removed 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.

 When a parenthetical element -- an interjection, adverbial modifier, or even an adverbial clause-- follows a coordinating conjunction used to connect two independent clauses, we do not put a comma in front of the parenthetical element.
 

The Red Sox were leading the league at the end of May, but of course, they always do well in the spring. [no comma after "but"] The Yankees didn't do so well in the early going, but frankly, everyone expects them to win the season. [no comma after "but"]  The Tigers spent much of the season at the bottom of the league, and even though they picked up several promising rookies, they expect to be there again next year. [no comma after "and"]