The tendency I see with my students is they want to play the tune up to tempo immediately. This doesn’t work. You must practice very, very slowly. By doing this you’ll hear where you are having trouble in different parts of the tune.
I can’t emphasize this habit enough!
Build up speed slowly. I realize if a tune is written in a fast tempo, slowing it down is sometime awkward. What you should do is play a fast piece you already know that’s similar, then work on the tune you’re learning.
One of the keys to success (and building confidence as well) is super slow practice. The process of practicing in slow motion, while being fully conscious, highly engaged, and thinking deeply about what you’re doing, is what works!
Incidentally, this is not a painful torturous process, but often an engaging and gratifying one. A way in that opens up the door to many satisfying little-discoveries that could be the key to getting a phrase to sound just the way it should.
The thing about slow practice is that it’s not just to slow things down in order to play it exactly right, it’s about fine-tuning the way it’s played, and looking for different ways to play it even better while you’re playing slowly enough to watch and think about the little details.
Remember: PRACTICE SLOW!!!