Learning tunes from a fake book is the hard way to go about things. Here is the Bill McBernie method of jazz practice in which you play by ear to multiple recordings.
I could recall the basic outline of the tune "A foggy day" from playing it years ago. That helped. (If you don't know the tune, you must listen until you can sing along.) Below are the recordings and the order in which I played them. Some were played numerous times as I recalled more of the melody and figured out the key. The song was played in the keys of F, C, Eb, and Bb. I played along on vibes, not piano. I focused only on the melody . As the practicing progressed, I began to recall and understand the chords.
Today I was playing it on the piano, from memory, with the chords.
You've got to learn your instrument. Then, you practice, practice, practice. And then, when you finally get up there on the bandstand, forget all that and just wail.
I'm a professional pianist and music educator in West Toronto Ontario. I'm also a devoted percussionist and drum teacher.