Wow, I'm glad you asked that question because the answer is pretty cool. So I did some reading:
Early Stuxnet Variants Used 'Cunning' Hack of AutoRun to Spread
It seems that early on, it used a vulnerability in Window's AutoRun routine. The autorun.ini file would exist at the root of a removable usb drive, cd or some other media. When inserted into a Windows system, provided the AutoRun settings were favorable for the worm, it would execute code hidden in very same autorun.ini file. It would also add an additional 'Open' command to the main Windows context menu (right-click an empty area on your desktop). When invoked, Windows would launch Stuxnet in the background while otherwise behaving normally. Microsoft has since patched this exploit.
Details of the early AutoRun exploit:
Stuxnet Before the .lnk File Vulnerability
In March of 2010, it seems, an upgraded version of Stuxnet began exploiting a Windows vulnerability having to so with the Print Spooler service. This exploit was first published in a Polish Hacking magazine and was in the public domain for at least a year before Microsoft did anything about it. This exploit has (finally) been patched as well.
Microsoft Missed 2009 Published Article on Stuxnet-Type Attack