The word origami almost always makes me picture the peace crane, a paper bird model that flaps it's wings. There are, in fact, many bird model besides the crane. All of these models, and plenty more, stem from a single base model, called appropriately 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.

The mountain folds cut the paper in half horizontally and vertically. Make the first fold, creating rectangle, crease well, and unfold.

The second mountain fold, perpendicular to the last, also creates a rectangle. Crease well, but do not unfold.

Put the crease in your hands, with one hand on either side of the center fold. Pinch the paper, and push you hands together gently. The folds you made before should collapse into a shape with four flaps.

You don't need to hold the model like this photo here, I'm just showing what it looks like from the top.

Instead you want to flatten the model into a diamond shape (which is really a square on a corner).

The finished model will have creases down the center of the back and front, and is a square the quarter of the size of the one you began with.

Practice this fold, it is incredibly useful. Flowers and animals of all sorts begin here, and if you ever try "freestyle" folding, this is a great place to start.