Double/Single Quotation Marks

Use single and/or double quotes when (in descending order of importance):

1) The style sheet or style specs used by your school or company specifically require their use in a case such as yours.
2) Your academic discipline has a standard convention that requires their use in specialized cases (and your case is one of these).
3) You are an ordinary writer and you:
a) are using U.S. Style. In this case, you use double quotes to indicate a directly quoted passage, and single quotes to indicate a direct quote within the first direct quote. Within those single quotes, if there is another direct quote, you use double quotes again. If you have even more direct quotes within your direct quotes, then for God's sake consider rewriting your passage. Or else just continue alternating nested single and double quotes. Place the punctuation that goes with the quote inside the pair of quotations that belongs to it.
b) are using U.K. style. In this case, do as specified in a) except for single, read double, and for double, read single. Place the punctuation that goes with the quote outside the pair of quotations that belongs to it.
c) are using U.S. style and you are setting off a word or symbol as an example, i.e. "This" is a word with four letters, "T", "h", "i", and "s". Set the punctuation outside in this instance ONLY.
d) are using U.K. Style, in which case follow c) except for single, read double. Set punctuation outside quotes in the usual way.

Overlooked something....

The use of "security" above is an example of quotes used as if you had in mind the word "so-called." Quotes used to express sarcasm should follow the normal rule for quotations in your context (work, school, country).

Are you using 'single' and "double" quotes in an essay? If so, look up the school's policy on usage. Individual schools (departments) within universities (colleges) often have different policies on the use of single and double quotes. These policies are formulated to confuse students and harass fellow academics :)
If you're using them in corporate/ government writing, look up your corporation's/ government department's policy on their use. Or the style manual your corporation/ government department uses.
If you're writing to be published by a commercial/ academic publisher, look up their policy.
If you're using them on your website, it's your choice.

I disagree with "online internet casinos" below.

Well, except that you really DO need quotation marks to make that HTML work correctly.

That's all.

And yes, you can quote me on that!