Designer "Tkamen" has created papercraft templates for the rings of power for each of the lantern corps, five of which are shown above. The PDO format templates may be downloaded here. The finished rings are rather large with a 1 1/2" (3.8 cm) diameter. I wanted a smaller scale Green Lantern ring, so I took the liberty of creating a scaled down version of the template in PDF format which is available here. Unfortunately, there are no instructions available for building the rings other than the PDO.
UPDATE 10/6/2012: The download above for scaled down green ring template now includes scaled down templates for the red and blue rings as well!