Punctuation. To the average writer, it is merely a form of style, but one should never underestimate these small dots and lines, for they represent the way we speak just as much as—if not more than—every letter of the alphabet. All proofreaders and any translator concerned about the quality of their productions should fully master the use of all punctuation signs used in their working languages. This is not meant as an exhaustive guide, but I will try to give you general tips and guidelines to keep in mind when writing in any language and for any purpose, based on what I have observed in some European languages.
Universal (?) signs
Periods (.) and commas (,) are the most common signs in Western languages. It is obvious that the period marks the end of a sentence, but also indicates abbreviations, provides structure in lists, etc. As for the comma, it is also well known, but often used in very questionable ways. Commas are generally used to insert rhythm in a sentence by isolating complements, structuring enumerations, enclosing parenthetical expressions and so on. I strongly recommend reading up on the comma to grasp all of its subtleties. If you are still unsure, read your sentence aloud and ask yourself: "would I mark a pause there when saying this?". And, of course, the question (?) and exclamation (!) marks are pretty self-explanatory; just make sure that you are aware of particularities such as the inverted question and exclamation marks of the Spanish language when you write in a foreign language—they may seem useless to you, but they are part of the language just as much as the words you translate.
More rhythm and functions
The semi-colon (;) is not very well understood by most. As far as rhythm is concerned, semi-colons are halfway between commas and full stops, much like colons (:). However, their use is totally different. Colons clearly introduce an enumeration, explanations or specific information mentioned moments earlier. Semi-colons, however, are used to replace conjunctions (and, but...) to introduce a new idea without cutting to a new sentence. Since the semi-colon is a very particular sign used in specific instances (sometimes, you really should start a new sentence or simply use "and"), you should try to avoid it when you are unsure of its relevance. A misplaced semi-colon will break the flow of the text in an awkward way, while you can easily replace it with a more common sign or different wording.
Parentheses are rather easy to use, as they simply introduce an idea of secondary importance in the flow of a sentence. A common mistake to avoid, seen especially when authors use parentheses inside parentheses, is forgetting to close them; another is putting punctuation that should be outside of them inside and vice versa.
But did you know that dashes do almost the same thing? Dashes—not hyphens (-), mind you—also indicate parenthetical expressions (secondary ideas that are not strictly related to the content of the sentence or that serve as a means to give additional information). Once again, I can not go into details in this article, so I recommend avoiding their use until you are sure that they are appropriate (especially since they can be replaced by parentheses quite easily). Another detail to pay attention to is that there are several dashes of varying lengths, and each serves a different purpose. To be honest, most people would not notice, but are you not supposed to strive for perfection?
One does not need to spend a lot of time describing quotation marks: used primarily in dialogs, quotations and to emphasize words or phrases, the only real difficulty to keep in mind is to use the right sign for each language and follow its rules. Many languages have different quotation marks than those used in English and sometimes have different rules regarding their place in the sentence or around words. Another detail is that some languages require different signs for quotations inside quotations for the sake of clarity ("The captain said: 'Hello!'"). As a sidenote, if you are writing dialogs (especially long ones), consider using dashes—one of them exists specifically for this purpose.
Even signs like spaces can have particular rules to follow in certain languages. Did you know that many French punctuation marks are preceded by a non-breaking space? Are you able to spot two spaces in a row? What about paragraphs, margins or indentation? Is there a fundamental difference between bold and italics? There are also some details that may seem trivial but that are more than "nitpicking". For example, apostrophes are mistreated very often in English (you certainly have seen "your" and "you're" being misused, for instance), while they have a strong influence on a sentence's meaning. Similarly, many languages have accents and special characters that sometimes give totally different meanings to words: do not neglect them!
It would not be reasonable to make an exhaustive article reviewing the punctuation of every language and the rules associated with it. This article's intent was mostly to warn every language worker that punctuation is not just a set of fancy dots and lines; now it is your duty to do your research in the appropriate language and learn the subtleties of punctuation. It's a lovely world of fine details and precision—or a painful nigthmare of trifles, depending on your tolerance to typographical hair splitting!