Learning to play the scales will help alot, as all melodies come from scales. It is also helpful to do some finger stretches like other string instrument players do. Some folks I know have opened up a Violin method book & learned the finger stretches they teach. Many classical guitarists are taught these type of hand/finger stretches. Best finger nimbler stretch I've found is sort of like to Vulcan hand salute! These are actual stretches away from your instrument.
    Hold up your hand palm away from you, & stretch your pinky away from the ring finger. Then stretch both the pinky & ring fingers held together away from the other fingers--the Vulcan salute! The pointing finger away from the middle, ring, pinky held together. & finally the thumb. Then reverse & go back through from thumb to pinky. Do with both hands, especially if you are a fingerpicker. For playing guitar in Ceoli bands, I fingerpick & play bass with thumb & rhythm with other fingers--with no pick. My pals from Ireland really liked that for most of the jigs & reels & hornpipes & polkas.
    The more your fingers are able to stretch, the more agile they will be. ALso, the more varied scales-major & minor-that you play in various keys, the faster you will be able to play any tune in any given key(for some real fun, learn all keys--Try not to get stuck in D & G & A). Find the scales under Play them stating on various srings. Another good thing is to find scales which are right under your fingers when playing the basic chords in each key-major & minor. Good luck!