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 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.

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.