s = s.Replace("\"", "\\\"");
or
s = s.Replace(@"""", @"\""");
In the first example the " has to be escaped with a backslash as it would otherwise end the string. Likewise, in the replacement string \\ is needed to yield a single backslash by escaping the escape character.
In the second example verbatim string literals are used, they are written as @"...". In those literals no escape sequences are recognized, allowing you to write strings that contain lots of backslashes in a much cleaner way (such as regular expressions). The only escape sequence that works there is "" for a single ".