Summarize this article:

Position your knife above the end of the shallot that has the small rootlets. Leaving the end barely attached will make the shallot easier to peel.  This should pull off a large section of the peel and leave other parts of the peel showing so that they can be easily grasped.

Summary:
Lay the shallot on your cutting board. Cut a slit that is deep enough to almost but not quite cut off the end. Position the shallot so that the rootlet end is on top and the wide end is on bottom. Grasp the rootlet end and pull it down toward the wide end of the shallot. Peel the rest of the shallot and discard the peels.