What do you do for a child who is experiencing growing pains?

Reassurance. Reassurance is number one. Secondly, if the pain is "severe", simple analgesics like tylenol (acetaminophen) or Motrin would normally suffice. Avoiding excessive sports activities, known to cause/aggravate pain may be sometimes helpful.
Supportive care. Provide support with heat pads, massage the area, and occasionally a otc children's pain medicine. The pain is real, so it needs to be taken seriously.