Quote - You guessed it, transparency is involved. But it isn't as simple as all that.

1. Your transparency map should, ideally, be more opaque where there are multiple layers of cloth, such as seams, collars, cuffs etc.
2. Not all colors become transparent at the same rate. If a character was wearing an outfit with a white background with a darker pattern, the pattern should be less transparent. Also, most colors darken when wet, so you probably want to change your base texture as well.
3. Wet cloth is often shiny, so you want to add some reflectivity in the material room to fabrics such as polyester and denim.
4. Wet fabric drapes differently. It tends to be both heavier (so it hangs lower), and also stickier. You might try using the cloth room and playing around with the parameters.

 

So I've been playing around with my suggestions. 

1. This is tricky -- it probably involves actually creating one's own transparency map to get right. The classic outfit which relies on this technique to get right is something like white slacks, which are often a little translucent to begin with. You have seams, the reinforcement for the zipper, the waistband, and often pockets. No easy fix here.
2. This is easier to do. You can generate a quick and dirty transparency map by inverting the colors of the texture map and grey scaling them. There is actually a way, more or less, to do this in the material room, but I can't quite remember it. You can then blend this transparency map with some appropriate noise.
3. You can darken stuff like denim by adding some grey in the material room. One issue is that if the figure is actually partially in water, the cloth which is out of the water will be shiny, but the cloth which is in the water won't be. You can make two renders -- one with the material shiny, but the surface of the water black with no reflection or highlights (this makes it easier to work with in post work), and the other with the water normal, but the cloth with no highlights. In postwork, layer the relevant parts of the first (shiny) render on top of the second.
4. Some materials work well in the cloth room. You need to increase parameters which reflect stretchiness, fabric weight, and fabric friction against skin, and decrease parameters which reflect how easily the fabric slides against itself and how easily it returns to normal shape. On the other hand, some things are difficult in the cloth room, most notably the tendency of some fabrics to get really wrinkly and bunch up, and also the clinginess (especially the tendency to cling to overhangs (breasts), and crevices (buttocks). For those you probably want to find the best conforming cloth.

A further note on cling -- wet clothing tends to cling, but once pulled away will hang pretty limply. However, wet clothing, especially light colors, are more transparent when touching something else than when even a slight distance away. (This is why wrinkles aren't transparent.) So if a woman is wearing a when shirt, which hangs loose in front, her nipples should be visible, but her navel shouldn't be.