I was playing with a bluegrass mandolin player gearing up for his first dance. One of his sets included the venerable Forked Deer. He confessed he was having some trouble with it, and worried he wouldn't be able to play it at the same speed as the rest of the tunes in the set. I suggested we try it. He launched into it, and his problem was clear. His version was all eighth notes, every note different from its neighbors. He thought he needed faster notes. He needed fewer.
Start by playing the simplest version of the tune you can. Arnold Schoenberg says, in his composition book, that if you pull out all the stops at the beginning, you don't have anywhere to built to. Good advice from a guy who writes tunes you can't listen to is still good advice.
The tricky part is learning which notes to drop.
There are notes you can drop and still recognize the tune. There are others you can't. How do you know which is which? I have no idea. This is true for most kinds of art. Consider, for example, the following two sentences:
Ynk Ddl wnt t twn, rdng n pny, stk fthr n hs cp nd clld t mcrn
a ooe e o o a ii o o u a ee i i a a ae i aaoi
I dropped the vowels in the first, and the consonants in the second. You can still read the first and tell what it's about. The second's line noise.
Like Potter Stewart's description of pornography, "I shall not today attempt further to define the kinds of material I understand to be embraced . . . [b]ut I know it when I see it . . . "[1] , I shall not try to define Forked Deer, but I know it when I hear it.
Guidelines? Notes on the beat are usually important. For any note-y tune you're struggling with, trim away every note that's not on the beat. Eighth notes? Gone. Ornaments? Gone. Passing notes? Gone. If essential notes have been cut out, playing the tune this way will make them jump out at you. Put those back in.
This is good practice for more than just learning.
When the fiddlers are playing a wall of notes, you can help the dancers or listeners hear what the real melody is by emphasizing one note or another. Next time you're listening to fifties rock, listen for the backup singers to hear how this works.
A mandolin looks like a fiddle with frets, but imitate the clawhammer banjo players. You can't put in all the notes playing clawhammer, so they have to figure out which ones to play.
Backup guitar is a place to practice this, too. As a change from bass runs, I sometimes play MBG ("Em-big") -- Melody Backup Guitar. I boom-chuck, but try to have each boom be the melody note in the tune on that beat. It isn't really melodic, but it backstops the melody, makes for an interesting bass line, and you could probably even name a lot of melodies just listening to the guitar.
A solid ripple of continuous eighth notes shows off technical virtuosity, but it always sounds to me like auctioneering -- you could train yourself to talk like that all the time, but who'd want to talk to you? Folks'd spend their time listening to how you were talking instead of what you were saying.
After you can play the tune simply, and hear its essence, then you can add notes to make it flow and bounce. Sketch the outline first, then color it in. Velazquez painted directly on canvas, alla prima, but most everyone else starts out with drawings and underpainting.