How can I get double quotes into a string literal?

Thankfully, with C++11 there is also the more pleasing approach of using raw string literals.

printf("She said \"time flies like an arrow, but fruit flies like a banana\".");

Becomes:

printf(R"(She said "time flies like an arrow, but fruit flies like a banana".)");

With respect to the addition of brackets after the opening quote, and before the closing quote, note that they can be almost any combination of up to 16 characters, helping avoid the situation where the combination is present in the string itself. Specifically:

any member of the basic source character set except: space, the left parenthesis (, the right parenthesis ), the backslash , and the control characters representing horizontal tab, vertical tab, form feed, and newline" (N3936 §2.14.5 [lex.string] grammar) and "at most 16 characters" (§2.14.5/2)

How much clearer it makes this short strings might be debatable, but when used on longer formatted strings like HTML or JSON, it's unquestionably far clearer.

Escape the quotes with backslashes:

printf("She said \"time flies like an arrow, but fruit flies like a banana\"."); 

There are special escape characters that you can use in string literals, and these are denoted with a leading backslash.