Playing the mandolin isn't like playing the guitar. While guitar players only need to use one finger per fret as they strum, the mandolin uses diatonic fingering, which means each finger plays two or three frets at a time. Diatonic fingering means the average right-handed mandolin player needs to constantly readjust the position of the left hand and fingers depending on what fret is played. Finger exercises help to train the left hand and learn correct positioning.
Fret by Fret
Play the first string on the mandolin with no frets. Play again with the index finger of the left hand on the first fret. Add the middle finger on the second fret and play again. Continue strumming and adding frets until all four fingertips of the left hand are on the fretboard. Then move backwards, taking each finger off the fretboard in turn. Repeat from the top for the second string, and so on through all the strings of the mandolin.
Place the left-hand fingers on the highest string, spacing each finger one fret apart. Then, simultaneously lift the index and ring fingers up and move them to the next string down. Lift the middle and pinky fingers up and move them down to the next string alongside the index and ring fingers. Continue alternating, walking these pairs of fingers down the strings until you reach the bottom string of the mandolin, then walk them back up.
Place the left-hand fingers high up on the fretboard. Position the index finger on the first string, the middle finger one string down and one fret higher, the ring finger one string down and one fret higher, and so on. Move the index finger down one fret, holding the other fingers still. Maintain space between the index and middle fingers, repositioning them with the right hand if necessary. Follow with the middle finger, then the ring finger, and so on to the end of the fretboard, then reverse. Practice maintaining space between the fingers as they move around the fretboard.
Practice playing with two fingers at a time to target and stretch specific fingers of the left hand that need training. Practice alternating up and down frets with the index and middle fingers, the index and ring fingers, the index and pinky fingers, and any other combination you like. Pay special attention to the pinky and ring fingers, as these shorter fingers can be the hardest to train and stretch.