Bird Base
The most famous of Origami is the peace crane, a paper bird model. There are, in fact, many bird model besides the crane. All of these models, and plenty more, stem from a single base model, the bird base. While the bird base is only four folds, and the starting point for the crane, starbox, fortune teller, and some flowers. This form also becomes dinosaurs and other animals. I've even made a scorpion from this simple base.
This square shape is made with four folds, two mountain and two valley. First lay down a piece of square paper. If your paper is colored, begin with the colored side facing you.
Here are all of the folds marked out. The dashed lines are valley folds (which are folds that hide the face, and create a valley with the paper), and the solid lines are mountain folds (which are done by flipping the paper over and doing a valley fold).
The first valley fold cuts the paper in half diagonally, forming a triangle. Make a good crease, and unfold the paper flat.
The second valley fold cuts the paper in half diagonally also, but perpedicular to the last fold. Once again, a triangle is formed. Crease well, and unfold the paper.