Well, the most basic steps(s) in weathering an AFV is a wash and drybrush. When you drybrush, use lighter shades, and on the lower undercarriage use lighter earth tones. I also mix a very thin but dark brown wash using tube acrylics. Then I use an old paintbrush or toothbrush to flick on this wash onto the vehicle. If you have an airbrush, you can use Tamiya Buff, very thinned, and mist the paint over the model, focusing on the lower parts. This stuff is excellent in representing dust.
Also, if you want actual mud, you can try the following:
Take some regular earth from your backyard, or wherever. Dry completely and grind into as fine a powder as you can. Mix with water and white glue (about 60/40 ratio) and make a thin mud out of this. Splatter the mud over your tank, into the tracks, and all over the running gear. When dry, you can paint or leave as is.