My ten-year-old daughter made a very fast (10-20 minutes) and pretty Asian-style fan, and this is the documentation of her project.
Tools and supplies:
paper (cardstock might be better)
two popsicle sticks
white glue (we used Aleene's)
a piece of tape (or, better, some cloth)
compass for drawing circle
pen and/or other drawing tools
optional: red string
Step 1: Cut a semicircle
Adjust the compass to the size of the popsicle stick.
Draw a semicircle (or a full circle if you want to make two).
Draw an appropriate design. E.g., a dragon.
Cut it out.
Glue a popsicle stick from the center of the semicircle (i.e., the place where the spike of the compass was) along the side.
Do a fan-fold, alternating folding directions until the fan is all folded up.
Glue on a popsicle stick on the other side.
Step 5: Join popsicle sticks
Now join the inner ends of the two sticks. My daughter joined them with tape. I would use a piece of cloth with a good quality glue.
Step 6: Optional: Tie up with red string
To make a nice packaging, tie a red string around it.