It's a little less graceful than the earlier NIN remix contests -- you have to download and fill out this PDF (which I would have Drunkpoet break down, but he's probably hitting the Manhattan strip clubs this weekend), then fax it, and then receive a CDR of the master tracks. Then you send back a remix, which Invisible Records will own throughout the world in perpetuity.
It looks like if you sign that contract, you have to deliver a remix of some variety by November 17, 2006. Good luck!
p.s. thanks go to poison_mouth for bringing this to our attention.