Plastic container of water. Use a shoebox size plastic container and stiff brush to clean those muddy RC tires. Fill the container with an inch or so of water and carefully lower the back or front tires into the water (or tilt the car if it's sitting on a car stand), spinning the tires to remove loose dirt and grime.
Stiff brush. Use a stiff brush -- like the kind used to brush the mud off your shoes -- to loosen the mud stuck in the tire treads. A small hard-bristle toothbrush would work too especially for getting into heavy treads.
Don't soak. When washing your tires (on or off the RC) don't leave them soaking in the water too long. Doing so can cause your foam inserts to get too wet and start disintegrating and can loosen your glue job if your tires are glued.
Plain water vs. cleansers. Water usually works fine but you can also use a little soap. Something simple such as dish detergent or a mild all-purpose household cleanser works well. Some RC owners advocate using stronger solvents such as turpentine or even a lubricant like WD-40. If you do so, use with caution. Using too much or soaking tires in these materials could soften them up too much or create a sticky mess.
Clean tires right away. If you wash your tires as soon as you've finished running your RC (after letting it cool down a bit) then water and a brush should be sufficient to get them clean. Don't give mud a chance to dry or it will be much harder to remove.
