There are a variety of methods:
For mud, I usually use the real thing. I sift very fine dirt from my back yard, and make mud out of it using water and white glue, then just splash on the model, based on reference pics.
As for dust, there are a few things you might try:
As mentioned above, either pigment powders, such as those from Mig, MMP, or Quartermaster will work fine. A similar (read: same) method is to buy pastel chalks, grind them up into powder, then use that.
My favourite method is using tamiya Buff paint. I can't remember the exact XF number.
Take the paint, and thin it. Thin it a LOT. I'm talking about 1 part paint to 6-7 parts water, if not more. If you have an airbrush, take this tint, and lightly 'mist' it over the model, concentrating on the lower hull and tracks.
If you dont have an airbrush, I suggest thinning the paint even more, something like 1 part paint to 10 parts water. Use this to 'wash' the lower parts of the hull and tracks and wheels. Do this generously. As the water evaporates, you'll be left with a fine dusty surface. You'll have hard edges from where you applied the wash, but if you're careful and attentive, as the paint is just about to go dry, you can drybrush with a completely dry brush
, and attempt to blend the edge away.
Hope this helps!