If you're an American, employing quote marks couldn't be much easier: Unless you are citing anything within a quotation, use double quotation marks at all times. It's not the same throughout the rest of the Anglosphere, where singles are used in books and doubles in newspapers.
In Europe, they also use single quotes for quotations. This is because back in the day, when paper was printed on by hand, a single quote could mean something different from a double quote. Thus, quoting someone would mean copying their words exactly as they had written them (or speaking directly to them!), not adding additional information (such as my example).
This isn't really relevant today since computers do everything for us, but I wanted to explain this because so many people get confused about what type of quotation marks to use in which context!
Now, back to your question: Use double quotes if you're quoting someone word-for-word, use single quotes if you're referring to part of a sentence or article.
As an added tip, there are three types of quotes: Single, Double, and Quotation. The first two are easy enough to identify as such, but sometimes writers use single quotes to indicate a quotation mark too. This is incorrect, but it does happen. If in doubt, assume you're looking at a quoted phrase until you find out otherwise.
Single quote marks are often used in British and Australian English. Double quote marks are commonly employed in North American writing. It is recommended that you use one type of quote mark over the other.
Use single quotes if a word or phrase comes directly from a source such as a book, interview, or conversation. Use double quotes if you're including a word in your own language even if it's common knowledge among readers or listeners. For example, if I said "New York is a city," that would be correct because I am including my own words in this sentence. If someone quoted me saying "New York is a big city with skyscrapers," then I would need to use double quotes because they are quoting someone else's words.
It's also important to note that some sources include both single and double quotes while others may only use one type of quote mark. For example, a newspaper article will usually only include double quotes whereas a book might use both types.
The choice of quote marks should be consistent within a document. Otherwise, readers will have to work hard to understand what's being said.
There are times when it's necessary to use multiple types of quote marks within a single sentence.
Double quote marks are used for direct quotations as well as the titles of works such as novels, plays, movies, songs, lectures, and TV programmes. They can also be used to convey sarcasm or to establish a new phrase or nickname. A quote within a quote is denoted by single quotation marks. Titles should always be placed in quotes.
Punctuation, Single, and Double For a citation within a citation, double quotation marks are used first and single quotation marks are used second in American English. Unless it is part of the quoted text, all punctuation in British English is put outside the quotation marks.
General Usage Guidelines Double quotes are used to express irony or an author's disagreement with a premise, as titles for short works such as TV series and essays, or as scare quotes to indicate irony or an author's disagreement with a concept. To enclose a quotation within a quote, a quote within a headline, or a title within a quote, use single quotes.
Single quotes are also used to express agreement or acceptance of a given premise, as in "Yes, 'this' is true". They are often used when referencing a specific word or phrase within the text. For example, one might reference "the blue car" by using 'car'. Single quotes are also used to express that something is not known or cannot be verified, like in ""This statement is false." Says who?"" They are also used when writing code or mathematical formulas where they need to be literal quotations.
Double quotes are used to express a question, an exclamation, or another form of discourse marked by its tone and intensity, like whispers or shouts. They are also used to attribute words or phrases to someone speaking directly to the reader (or listener), like in "I told him to be careful, but he didn't listen." Finally, double quotes are used to express a quotation within a quotation, like when Shakespeare says, "All's well that ends well."
Single quotes are also used to express a question, an exclamation, or another form of discourse marked by its tone and intensity, like whispers or shouts.