Watch the Am to F online guitar lesson by Brad Carlton from Guitar Lab: Super Sustain
This lesson deals specifically with the melodic moves that exist between the Am to F chord change. Diagram 6 shows these moves which involve common tones, ascending moves, and descending moves. I've included notes outside the realm of triads. To use this chart simply find the note in the column under the Am chord and play it during measure three. When the chord changes from Am to F, follow the arrow to the appropriate note in the column under the F chord and play that note. Set a goal for yourself to clearly visualize the new note so that you can play it precisely on beat one of the new measure. Once you establish this you can play more freely and still zero in on your target note. Be sure to capitalize on common tones by sustaining the note and not re-striking it. For all ascending moves apply the following techniques: picking the new note, hammering on to the new note, applying a legato slide to the new note, and bending up to the new note. For all descending moves apply the following techniques: picking the new note, pulling off to the new note, applying a legato slide to the new note, and releasing to the new note. This last technique requires that you played the first note (over the Am chord) with a bend. You can then release to the note for the F chord.
As in all of the other lessons be sure to apply this information over the entire fingerboard.