It depends on the pillow.
If you have the Casper Original Pillow, you'll unzip the cover and take out the inner pillow. Zip the outer pillow back up, and put both in the washing machine. Use the cold water setting and, if your machine has it, select the extra rinse setting. In the dryer, use the tumble dry setting, and toss in a few dryer balls.
Other pillow models may have different instructions. Read the tag before putting anything in the washing machine or dryer.