September has 30 days (remember the rhyme: 'Thirty days hath September...'). In a leap year, February has 29 days instead of the usual 28. Adding these gives 30 + 29 = 59. The key is knowing both the September day count and the leap year adjustment for February.
September always has 30 days, and February in a leap year has 29 days, so 30+29=59. The trick is remembering that 2000-era leap year rules give February the extra day, which is what pushes the total from 58 to 59.