So, I decided to start with the lightest color of all, white, and wash it, seeing what the effects were. As flesh color is something I paint a lot of lately (I am painting ancients at the moment, so there is a lot of flesh to be painted). For painting flesh, Citadel offers three basic colors: Flesh, Sepia, and Mud. Over white, Flesh gives a reddish, sun-burnt hue, Sepia fives a orange-brown hue, and Mud a darker-brown hue. By the way, the Black wash gives a gray hue over white.
The good thing about Citadel washes (or bad, depending upon your point of view) is that one coat will not do. Like painting with watercolors, that means you wash with one color and then wash with a different to get a different shade. You can also mix them together. For example I mixed Green and Mud and made a nice Olive color. By using Privateer Press' Yellow ink and putting Mud as the second coat, I got a good Dark Mustard color.
For some figures that are deeply cut, it may take more than two coats. I use small brushes to apply the washes, that way I can move pools of wash, lightening or darkening areas, as necessary. If I do a third coat, it is usually only to specific problem areas (shin, elbows, noses, and ankles) so I don't darken the other areas too much. For figures that are not cut at all, for example old Scruby miniatures or some of the simpler Irregular Miniatures sculpts, washing won't work at all as the figure would be uniformly the same color.
Ultimately, that is the point of washing: darken the recesses while keeping the highlights lighter, effectively shading the figure without a lot of effort. Washing does that for you, but it is not as simple as dipping. On the other hand, washing produces better results, in my opinion.
Pictures to follow.