Cardigan is sized by using different size needles to achieve a different gauge.

Small - 1 pair each US size 5 (3.75) and 10 1/2 (7mm)
Medium - US size 6 (4 mm) and 11 (7.5 mm)
Large - US size 7 (4.5 mm) and 13 (9 mm)

US crochet hook 3.5 mm (E)
7 buttons

Gauge:
4 stitches and 5 rows = 1” on size 10.5
7 stitches and 9 rows = 2” on size 11
3 stitches and 4 rows = 1” on size 13

Small = 32-34” bust (Finished 34.5”)
Medium = 36-38 bust (Finished 38.5”)
Large = 40-42” bust (Finished 42.5”)