Take your son's Sketchers outside, and bang them together at the soles. Do this until all large chunks of dirt break away.
Loosen the smaller pieces of dirt by going over them with a soft-bristle brush. Once you have the majority of the dirt removed, you can begin cleaning the Sketchers.
Wet an old rag with cold water. Drip one drop of mild dish soap on the cloth, and squeeze the cloth a few times to combine the soap with the water.
Wipe down the Sketchers with the wet rag to remove the rest of the dirt. You may need to stop a few times to wet the rag again.
Set the Sketchers out to dry, but don't put them in direct sunlight. The sun could fade the color of the sneakers.