First, you'll need to get a square piece of paper. For those of you who don't know how to make a square piece of paper, fold the top edge along the right or left edge making a triangle. Then, cut off the extra flap.
With your square piece of paper, fold it diagonally both ways and in half both ways. You should have a star shaped bunch of creases.
Now, you are going to make a preliminary base. Unfold all of your folds and fold it along one of the diagonal creases again. Your 'triangular' shaped paper should have a crease in the middle of the triangle. Fold this crease again to reinforce it. Unfold, and hold up one half of the triangle so your paper is 90 degrees. For the triangle that is pointing up, open it and flatten it top down. this will form a 'diamond' shape.
Do the same on the other side.
You'll notice with your 'diamond' that two edges are open and two edges are closed. Place your paper on your desk so that the open edges face you. Now, fold the bottom or the 'open' edges to the center. Do the same on the other side. Unfold.
Lift the top layer of your diamond and fold the paper in along the creases you just made then fold the top edge back so you have a long diamond. Do the same on the other side.
Now, you should have something called a bird base. From here, you can make two different types of cranes but I'll show you the one I prefer.
Now, your long diamond should be conjoined at the top half and the bottom half should be broken into two halves. The side with two halves should also be facing you.
Like before, fold the edges of the bottom half to the center and do this on the other side.
Now, this part may be tricky as you are going to do something called an inside reverse fold. Fold the first layer of the right side to the left like a book and then fold the bottom half up. Now fold the same 'book page' back to the right and fold the left page to the right. Like before, fold the bottom half up. and turn the flap on the right to the left. Now, you should have a triangle again with a rectangular bit on the bottom.
On either side of the triangle are two long pieces. Hold one side of model and pull the long piece of the other side out. This piece will be the neck so pull it out as far as you please but don't exceed 90 degrees. Once you've reached your desired angle, fold the base of it down. Do the same with the tail.
Go back to the neck and make the head. This will require another inside reverse fold. Like before, open the neck, fold down the top part of the neck, (the amount you fold down will be the length of the head} and close the flaps. Grab the head and pull it out to the desired angle and flatten it.
Turn your model upside down and you'll find a little hole. Put your finger on the pointy bit, or the cranes back, and blow into the hole while putting pressure on your finger. (Considering where the hole is, I found this bit funny too.) This will flatten the back.