I've seen this project called One Hundred Paper Cuts, and I'd like to report a paper cut, but don't know how. Can someone please tell me how to go about doing this.
Reporting a paper cut is just like reporting a normal bug, which is explained here.
Once you've reported the bug according to those guidelines, there are a few more steps to follow to upgrade it to a paper cut.
The bug is now reported as a paper cut.