Traditionally, the full-stop marks the end of a sentence but can also be used stylistically to mark staccato-like pauses in a sentence, as in the following example: "I. Am. Not. Happy. With. You."
It is also used to mark the end of certain abbreviations such as 'etc.' and 'et al.'. In British English, this is only when the abbreviation does not finish with the last letter of the abbreviated word. For example, the words 'doctor' and 'mister' end with the letter R, and so a full-stop is not necessary for the abbreviations 'Dr' and 'Mr'; however, with the recognised abbreviation for the word 'etcetera' (a word ending with the letter A) being 'etc.', a full-stop is needed. Similarly, if only the first letters of an abbreviated term are used in its abbreviated form, such as with 'AM' and 'PM' or 'SOS', capitalisation of these letters is preferred, and a full-stop is unnecessary.
Contrary to popular opinion, the comma does not indicate a pause or a 'time to breathe'; instead, it should be thought of as an indication of a slight change in tone.
Commas indicate the separation of items or clauses to better understanding of a sentence.
They are also used after certain connectives, adverbs and discourse markers (such as 'however', 'instead', 'for example', 'I mean', 'well', 'suddenly', 'firstly'…) and before certain exclamations and tag questions (such as 'then' in "Well, you do it, then!" and 'Don't you?' in "You do like me, don't you?") to differentiate such extraneous information from the principal text.
For advanced uses, see The Oxford Comma.
The ellipsis indicates a passing of time, a pause in the flow of speech, a trailing off, etc.
It can also imply a change in mood, tone, or volume (usually in decrease).
The question mark
The question mark indicates that presence of a question.
It is also used to mark rhetorical questions such as 'How dare you?' and 'How do you do?'
The exclamation mark
Similarly to the question mark, the exclamation mark indicates the presence of an exclamation.
The colon is used to introduce information.
Contrary to popular belief, the semi-colon does not simply join together two sentences that could exist perfectly logically alone; semi-colons mostly always replace conjunctions.
They can also be used to mark antithesis (the direct contrast of two opposing ideas) such as in 'The men went right; the women went left'.
They are also used in complex lists.
For more information, see How to Use Semi-Colons.
Curved brackets are used to supply the reader with [mostly useful] supplementary information.
The square bracket is used to provide the reader with supplementary information that is not entirely necessary or to note a supplementary opinion of the reader that is not necessarily factual.
It is also used in quotations to mark paraphrasing, clarification (for unspecific pronouns, for example) and pauses, etc.
“ ” or ‘ ’
Traditionally, the former is a quotation mark and the latter is a citation mark, but writers have come to use both interchangeably and so both are now acceptable as quotation marks. However, “ and ” can inform the reader of the writer's prejudice against certain terms and their usages, whereas ‘ and ’ can seem more neutral. For example: I think this "actor" is rather rubbish! vs The so-called 'factory' has been in operation for many years.
These are placed at either side of a direct quotation.
When quoting someone within a quote, one must use the opposite quotation marks one has used to open the quotation, to differentiate the two accordingly. For example: ‘Joanie said to me, "I'd rather you didn't do that!"’.
NB: Some writers use ‘ and ’, instead, and this is perfectly acceptable.
The hyphen or The n-dash
This mark is used to form compound nouns and adjectives.
For more information, see Hyphen vs Dash.
The dash or The m-dash
This mark is used to separate additional information (usually with a shocking or surprising undertone) from the main text.
For more information, see Hyphen vs Dash.
Originally the final letter of the alphabet, this mark is now used in place of the word 'and', but its use is limited to informal literature and marketing industries.
This mark is used in lieu of the word 'or' to note an interchangeability between two items.