But knowing all those fingerings won't get you where you want to be; you have to practice lots of different patterns with good hand position to play quickly and smoothly. We recommend starting with some full-range scales, major and minor. Then learn those scales in thirds, fourths, and even fifths! Arpeggios are great too; anything you can do to get your fingers moving on a regular basis! Here are some great method books that will take you above and beyond that book everyone uses in band: The Saxophonist's Workbook, by Larry Teal, 25 Daily Exercises for Saxophone, H. Klose, and Top Tones for Saxophone by Sigurd Rascher.