There are multiple reasons you might want to do this. It can create the appearance of texture, or create detail in a large empty surface, it can look like wear, scratching, peeling, and is a great way to add environmental effects like mud, rust, camouflage and so on.
The best way to do this is use a sponge, though a rough brush with stiff bristles can also work... Any sponge will do, though it's easier if you tear them to be smaller or different textures, you can also buy fancy sponges at art or bath and body stores.
Lucky for us, virtually every miniature we buy comes with a sponge.
Start by dipping your sponge in paint, and blotch off the excess with a few strong presses against a cloth or some paper. Kind of like getting the extra paint off a dry-brush, but not removing quite as much.
Once the excess is off, you can stipple to your hearts content. Use a light amount of pressure... notice the blotch in the bottom right of the following picture, how rough it is - even after all those small stipples, enough pressure still applies too much paint.
It's ok if you get some larger spots too - again, this is all random.
This technique will also work with watery or thinned paint. Like normal, the first few spots will be too strong, but quickly becomes usable.
Using this technique to layer similar colours is an excellent way to quickly add some high quality texturing to any larger area.
Also, a contrasting colour still looks natural when applied this way.
And here's a close up with my digital microscope of a couple places I used this technique on my Impaler's leather armour. As always, a light wash afterwards is a great way to tone down and blend together paint that stands out from techniques like this and dry brushing.