Or: How to produce organic shapes from a flat piece of paper
The hows and whys
One of the challenges of folding origami models is to create a result, which not only captures the basic features of a creature, but also does so in a fairly lifelike manner. Straight lines and flat planes make up the visual features of origami while in most chunks of organic matter they do not.
The problem of rendering a curved surface using flat components is not entirely unknown, 3d modelers face the same problem. In paper folding however, one is not necessarily limited to only flat surfaces.
Unfortunately it is not as easy as gently bending or shaping the paper so that it acquires the desired curvature. The paper "remembers" folds because the fibers in the sheet are broken along a straight line, this causes them not to return to their original position, and it is here the core of the problem lies. The fibers of the paper will not simply retain any shape unless they are actually more or less broken.
As the technique in question is named wet folding water is quite obviously a major component. This is because the stuff binding the fibers of the paper together is usually water-soluble. By moistening the paper the binding material lets go of the fibers enabling the paper to be shaped in a desirable manner without promptly returning to an approximation of its previous shape. Even better, when dry the binding material reforms and the shape becomes permanent.
The dos and don'ts
A step-by-step how-to for this would be superfluous; all there really is to it is basically "just add water" followed by folding. Instead I will list a few things that may prove helpful.
This technique works best with a fairly heavy type of paper since it is frustratingly easy to tear the wet paper
Before actually folding anything find out how the paper reacts to water, some types of paper have non-water-soluble binding materials.
Since the paper will expand somewhat when wet it may be a good idea to moisten it before cutting it to a workable format, the grain of the paper will cause it to expand more with the grain.
Speaking of wet, it should be called moist folding, as the paper ought not to have more water added to it than needed to temporarily dissolve the binding material. I would suggest using a sponge or piece of cloth to moist the paper.
Know exactly what you are doing, the paper will not stay moist very long and speed is of the essence. Extra creases will also only weaken the paper, which will greatly increase the risk of tears.
Use some form of clamps or other suited objects to keep the paper in the desired shape while waiting for the model to dry or while working on another part of the paper.