From the artistic realm of style we move suddenly to the technicalities of punctuation. Here there is greater scope for explicit rules, even if their correct application ultimately requires its own kind of art.
Quotation marks and other punctuation marks.
Do commas, periods, etc., go inside or outside of quotation marks? In so-called American Preferred Style, the answer is straightforward. Commas and periods always go inside quotation marks. Always. Without exception. Colons and semicolons always go outside quotation marks. And question marks and exclamation points vary according to whether they are logically part of the quoted material. This rule may seem illogical (it evidently developed as a way of saving space in typesetting); but it remains the preferred rule.
Internal and external.
In American style, primary quotations take double quotes. Internal quotations (quoted material within a quotation) take single quotes. Further nested levels simply alternate double and single quotes.
Block quotations.
As a general rule, quotations longer than eight lines should be set off from the main text -- indented and single spaced. Do not put quotation marks around such indented text. Remember that setting the quoted material off from the main text does not make it logically separate from the main text; that is, punctuate and capitalize the quotation (and use ellipsis) just as if the quote were part of the main text. Avoid prefacing quotes with expressions like "Adam Smith wrote: ..." Try to integrate the block quote into the text. Introduce it with a complete sentence like "Adam Smith argued this way." Or use the following trick. "The statesman," wrote Smith, who should attempt to direct private people in what manner they ought to employ their capitals, would not only load himself with a most unnecessary attention, but assume an authority which could safely be trusted, not only to no single person, but to no council or senate whatever, and which would nowhere be so dangerous as in the hands of a man who had folly and presumption enough to fancy himself fit to exercise it. (Smith, 1776 [1976, p. 456].)
Note also that the text following the block quotation should not be indented unless it is logically a new paragraph.
Mathematics.
An equation is syntactically a sentence or part of a sentence, and requires the same punctuation as a verbal expression: commas, semicolons, and periods.
Hyphenating after adverbs.
In American usage, one is not supposed in principle to hyphenate between an adverb ending in "ly" and the adjective (or participle) it modifies. For example, it's the "theoretically predicted value" not the "theoretically-predicted value." You should hyphenate in other cases. But notice that the hyphenation occurs only when the compound modifies the noun directly -- not when it is used as a predicate adjective. Thus, "the semicolon is a much-misused and oft-neglected punctuation mark"; but "the semicolon is much misused and often neglected."
The semicolon.
As I was saying, the semicolon is a much-misused and oft-neglected punctuation mark. It is used to separate two clauses that are complete (that have their own subjects and verbs) but that do not require the force of separate sentences. When to use a semicolon is thus a matter of style. Also, semicolons should be used to separate items in a list when those items are relatively complex or when commas would be confusing.
The colon.
Some people would argue that a colon should be used only after a complete clause. I wouldn't go that far; but it is true that the colon ought not to be relegated to introducing lists or equations. The effect of the colon is to concentrate the force of what went before into what follows. As such, it can be used legitimately in a wide variety of creative ways.
The question mark.
Remember that the question mark is a full-fledged punctuation mark, with all the rights and privileges appertaining thereto. That means that you never need to follow a question mark with a comma or a period. It's "What time is it? he asked," not "What time is it?, he asked."