Hey Phil,
I would divide the piece into 4 bar sections and master 1-4, then 5-8, then 1-8. Once you get that down (played cleanly and in-time) I would go up by 5% increments. Most tunes can be broken into 8 bar sections, in-which you can practice each section as described.
Furthermore, you can start to piece larger sections together. For ex: 1-16.
Hope that helps!
Drew