Choose the fake book that is most appropriate for your goals. There are a plethora of fake books available, from jazz and blues to classical and pop. Although you may play several genres of music, you should have an idea of what type of music you will play given the setting of your gig or performance.
Choose a set of songs you are somewhat familiar with, or that people will expect you to perform. Try making a set list of songs you will play at your performance, and give them a rough order. Spread out slow and fast tunes so you have a contrast of musical styles in your list.
Analyze each lead sheet you have chosen. You should have an idea of what the songs sound like, but if you don't, many lead sheets in a fake book will have general style guidelines in the upper left hand corner. These might list the style as "funk" or "swing," letting you know the time feel and giving you an idea of suggested tempos at which you can play the tune.
Start learning one of the songs from the lead sheet. Generally, the layout of a lead sheet will be melody and rhythm on a single staff, with the harmonic progression, or chords, on top. Sometimes the writer will include a bass clef part, if it is essential to the song. If you can already read music, it is just a matter of learning what each chord abbreviation means. The abbreviations generally are evident; for instance, a C major chord often is abbreviated as simply "C."
Practice learning additional tunes from your fake book. The more lead sheets you learn to play, the faster you will be able to learn new ones, and the better your sight reading will get, which will help when you are asked to play spur-of-the-moment requests. This takes time and patience, but is rewarding in the long run, when you are able to have a vast library of songs at your fingertips.