Source : Webster's Revised Unabridged Dictionary (1913)

Fingering \Fin"ger*ing\, n.
   1. The act or process of handling or touching with the
      fingers.

            The mere sight and fingering of money. --Grew.

   2. The manner of using the fingers in playing or striking the
      keys of an instrument of music; movement or management of
      the fingers in playing on a musical instrument, in
      typewriting, etc.

   3. The marking of the notes of a piece of music to guide or
      regulate the action or use of the fingers.

   4. Delicate work made with the fingers. --Spenser.

Finger \Fin"ger\, v. t. [imp. & p. p. {Fingered}; p. pr. & vb.
   n. {Fingering}.]
   1. To touch with the fingers; to handle; to meddle with.

            Let the papers lie; You would be fingering them to
            anger me.                             --Shak.

   2. To touch lightly; to toy with.

   3. (Mus.)
      (a) To perform on an instrument of music.
      (b) To mark the notes of (a piece of music) so as to guide
          the fingers in playing.

   4. To take thievishly; to pilfer; to purloin. --Shak.

   5. To execute, as any delicate work.

Source : WordNet®

fingering
     n 1: the placement of the fingers for playing different notes (or
          sequences of notes) on a musical instrument
     2: touching something with the fingers