Wing it

To perform an act, such as to give a speech, without the usual preparation. To improvise or ad-lib.

Improvise, as in The interviewer had not read the author's book; he was just winging it. This expression comes from the theater, where it alludes to an actor studying his part in the wings (the areas to either side of the stage) because he has been suddenly called on to replace another. First recorded in 1885, it eventually was extended to other kinds of improvisation based on unpreparedness.