Clean your dirty cleats immediately after a game, if possible. The longer the cleats sit, the tougher it can be to clean them.
Hose down the cleats with a garden hose. Getting the upper part of the shoe even wetter is not a problem. They are most likely dirty and wet to begin with, so a little more water is not going to damage the shoes.
Remove patches of mud or dirt on the cleats themselves with a wire brush, which can be purchased at a hardware store. This helps clear the cleats, especially if they are made of metal, of any debris that water or your fingers could not remove.
Let the cleats air-dry completely when possible. Placing them near a dehumidifier works also. However, placing them near a radiator or in the drier can warp the shoes, especially if they are made of leather.
Spray 409 onto the cleats if they are metal and if you are still not satisfied with results from the garden hose or wire brush. A container of 409 can be purchased at your hardware or grocery store. Let the cleaning solution cover the metal cleats for 30 seconds, then wipe off with a soft cloth.
Keep a putty knife in your bag or nearby during games. Running the blade down the shoe can temporarily clean the cleats of any caked mud on a rainy day.