This has been discussed at length on the Apple support forum - you could check it out there.
The short answer is that right now the ability to share reminders is no longer available on iCloud.com. The only place it can be accessed is in Mountain Lion 10.8.2 - which is no use to PC and iOS users.
Any existing shared reminders will continue to function.
Many people have sent feedback to Apple on this omission in iCloud 2.0.
I'm disappointed. I really hope the function is re-implemented.