Let mud fully dry on the suede, then brush vigorously back and forth with a stiff nail brush. Make sure to angle the brush into all crevices. Use a nail file tip or other pointy object to dislodge mud from hard-to-reach areas.
Use a softer suede brush to rub the scuff back and forth until the suede's nap is restored. Gently lift pressed-down areas with the tip of the nail file.
Spot clean suede shoes with a pencil eraser, small rubber eraser or a suede cleaning block. Once the spot is removed, use a suede brush to restore the nap around the area.
If suede shoes have become discolored because they got wet, the answer is wetting the entire shoe. Remove the laces. Gently rub a soft, damp sponge across the entire shoe. Keep the shoes minimally damp. Stuff the shoes with white tissue paper to hold their shape while they dry.
Once suede shoes are clean and dry, spray them with a suede protector to prevent further staining, spots and discoloration in the future.
Spray any new suede shoes with protector so they start out with an advantage.
All the supplies can be purchased at shoe stores, home shops and general stores. Some stores may sell kits with everything you need to clean suede.