Presoak
Let the clay stain dry thoroughly before you begin. Brush off any loose clay once the stain has dried. Be careful not to grind it into the fabric. Soak the stain in a commercially available enzyme presoak, or make your own solution by adding 1 cup of bleach to 1 gallon of water. Don't use bleach on anything but whites that are primarily made from cotton. If you must remove clay stains from other fabrics, substitute ammonia for the bleach.
Wash
Rub the stain with Murphy Oil Soap. Wait 15 minutes, then rinse with cold water. If you prefer not to use Murphy Oil Soap, add 1 tbsp. borax to 1 cup of water, rub it into the stain, wait and rinse with cold water. Launder in your regular wash cycle. Don't throw the clothes into the dryer if the stain persists; re-treat them.
Other Remedies
If the above method doesn't work, swish the whites in a mixture of hot water and a scoop of OxiClean. Then remove the clothing from the water, and rub the stain with a bar of Ivory soap. Pour baking soda onto the soapy stain, and scrub it. Rinse the clothing and add it to your regular wash. Repeat the process if the whites come out of the wash with any remnant of soil.
Another alternative is to make a solution of ¼ cup of soap, scraped from a bar of Fels Naptha, and 1 cup of water. Mix this solution thoroughly in a blender or food processor or with a hand mixer. Pour the mixture on the stain and let it sit for several hours. Throw the clothing in the washer with the rest of your dirty clothes. The Fels won't hurt colors. You can find it in the laundry aisle.