In English, when should one use single quotation marks vs double quotation marks?

Example: In Macbeth the First witch said
'Give me,' quoth I:
'Aroint thee, witch!' the rump-fed ronyon cries.

To put this in your essay as proof:
"'Give me,' quoth I:
'Aroint thee, witch!' the rump-fed ronyon cries." (citation goes here in MLA or APA or other format)

Use double quotation marks (") when quoting someone, taking information from somewhere, usually excerpts from books/magazines/articles/other sources of info.

Use single quotation marks for phrases used a lot, or when using words to give an underlying message that you want your readers to understand, but not take literally. They are also used in headlines and to show a quote within another quote.

For example:

Double quotation (I made all this info up):

A new study shows that a new species of genetically modified plants can live longer. They prove these plants can "sustain a longer life, while still functioning as any other plant would," says a scientist.

Single quotation:

"Ugh, he's so clueless. Did he ask you another 'smart' question again?

:)