Learn the tunes one part or phrase at a time, start slowly and cleanly and begin to pick up speed, practice that until it's in there good and your fingers know it without your thinking about it, then move onto the next part.

Find the bits in it that give you the most trouble and run over those alone over and over till they're smooth. Then play them in context i.e. the whole tune or part.

But don't overpractice it. Take a break from it for a few days and you'll be surprised at how the unconscious mind will have progressed on things while you aren't actually playing the tune. Visualization of you playing the tune and keeping the melody in your head is also a big help.

Another big help will be to learn the same tune on another instrument... what I call musical cross-training. Works for me to learn it on guitar, mandolin and whistle, if I can.

Important to play it slowly and get it right before increasing the tempo. "First comes right; then comes fast." Forget where I heard that. Some movie.