You'll need to get proper washi paper to do this, as western wood-pulp paper is too weak. You can also use silk, but washi is more widespread.
The ribs are made from thin strips of bamboo. They form the shape of the lantern by using a collapsible frame, much as a dressmaker uses a dummy:
Once the bamboo strips are all in place and the glue binding the ends is set, the outer layer of paper is applied. I can't help you with the kinds of glue used in traditional methods, but you might want to give wallpaper paste a try.
Once the paper is dry and glued to the bamboo frame, the inner support "dummy" can be collapsed and removed.
Notably, the chochin is not painted until after it has been assembled.
You might want to give Tuttle publishing a try:
Info@tuttlepublishing.com - they may have a book with relevant techniques, as they do a couple of papercraft books on making bowls and decorations with washi.