Ok, so now I know the basic folds. Now what?
The next step in folding an origami model is the choice of paper to use to fold for that specific model. There are a variety of different papers one can use to fold something. Different designs may be folded better with different papers and different people prefer different kinds of paper.
To start off, let's address a paper that almost everyone has readily available: computer paper. This paper can be used to make simpler designs such as a paper airplane or boat. Many designs require a square sheet of paper. To make a square sheet of paper with the rectangular computer paper, you have to take a corner of the paper and fold it down diagonally so that the shorter side of the paper adjacent to the corner matches up with the opposite longer side of the paper. Like so:
Next, you should remove the bottom rectangular portion either by cutting it off with scissors or by folding it up and then ripping it off. Next, by unfolding the diagonal, you would obtain a square sheet of paper.
Computer paper is often too thick and the creation of your own squares can result in squares that do not really square with sides being too long, sides that are not straight, and angles that are not right. Luckily, premade square origami paper can be directly bought. This paper can come in many different sizes, colors, and even designs.
Origami paper comes in a wide range of colors.
Standard origami paper can be used to fold a variety of designs, however, for more complex origami, this paper is still often far too thick and small to be used to fold intricate designs. A paper that I often use is tissue-foil paper. It is a thin paper made from layering tissue paper (not what you use to wipe your nose, but rather the tissue paper for wrapping gifts) and some sort of foil such as aluminum foil to make it so that the paper is thin while still maintaining its strength. Due to the foil of the paper, the paper maintains its creases very well, making the model much easier to collapse (to form the model) after the pre creasing (making preliminary folds that you unfold as a base for the entire model). This paper is often utilized to fold super complex models such as the phoenix by Satoshi Kamiya.
The origami phoenix designed by Satoshi Kamiya.
Other types of papers are also used to fold complex origami models such as Kraft, Biotope, Tant, Duo Thai, Washi Deluxe, and many more. All of these different papers can be ordered online.
Besides choosing paper based on its thinness and size, many models also take the paper's properties into consideration. For example, Jeremy Shafer utilizes cardstock to fold his origami Frog Tongue. By utilizing the paper's natural hardness, he is able to create a model that is able to shoot out like a frog's tongue and then retract.
There are a variety of different papers to choose from. I recommend that you try out different papers until you find the one that you like best.