If you have caked on, hard dried mud inside the case, consider using a sharpened wooden dowel rod to break it up first. Otherwise, throw it into an old milk jug with a squirt of dawn and warm water. Shake for a couple minutes, drain the water, refill with clean warm water, and shake about a minute more. If the water comes out clear and soapy, proceed to rinse with cold water. If the water comes out really brown or muddy, repeat the process, and then rinse with cold water until you have no more soap bubbles. Dry, size, load, shoot, repeat.
I have actually reloaded some 38 special brass close to 20 times without cleaning at all. Brass doesn’t have to be shiny and new, it really just needs clean primer pockets.