While there are many instructions for making the traditional Japanese paper "peace" cranes, these instructions will make a flapping bird - a moving model.
Step 1

Make or acquire a square piece of paper. To make your own square paper, fold a sheet of paper so that it makes a triangle.
Step 2

Cut the excess paper away.
Step 3

Fold the paper diagonally in both directions from the same side of the sheet, making two "valley" folds.
Step 4

Unfold and turn the paper over.
Step 5

Fold the paper in half horizontally and and then vertically from the other side of the piece of paper.
Step 6
Bring all of the corners into the center and fold the paper into a square.
Step 7
Fold all the OPEN edges to the center line. Make sure each of the edges are aligned with the center line. Repeat for each open edge.
Step 8

Gently unfold the edges.
Step 9

Tuck the corner into the inside of the paper, and do this along the creased lines.
Step 10

Do this for all of the open edges.
- You will end up with a kite shape.
Step 11
Take the top flap of the more acutely pointed end of the kite and gently fold it down until it's smooth. Repeat with the reverse side.
Step 12

Hold your new "diamond" shape with the split end up. Gently pull down one of the split ends and fold it so that it points straight out at a 90 degree angle from the rest of the diamond.
Step 13

Repeat last step with the opposite side (split) point. Turn the figure over.
Step 14

Pull down the "head" and reverse its crease toward the neck.
Step 15

Lift the "wings" and curl them slightly.
Step 16

Make your bird flap its "wings" by holding the chest of the bird with one hand and gently pulling back on the tail. Enjoy!