My preferred way to shingle a Gazebo Roof is to apply and trim the Shingles before assembly as shown in this instruction (starting on page 10).

Octagonal Shingles (4 different 'Starter Courses')
Traditional style
Classic style
Victorian style
Cottage style (with ¾" reveal)
  1. Flashing and Guidelines (here)
  2. First Course
  3. Weave, Flattening, Top Course

Details and Techinques:
  Drip Edge and Valley Flashing
  Dip-Scoop-Slide (applying shingles)
  Top Course ("Reveal")
  Boston Lap
  Sandpaper on a stick (trimming the edge)   

Sales:
  Pine Octagon Shingles (1000):  (500)
  Red Cedar Octagon Shingles:
  Dye1 Reddish Brown:
  Dye3 Dark Grey:
  Copper Sheeting for flashing: