How to teach a child to deal with his panic attack when he is by himself?

You can't: Panic attacks are fragmented fight-or-flight reflexes initiated normally in a dangerous situation for survival. Poor diet, especially sweets, makes the control mechanisms in the brain too reactive and the reflex activates for no obvious reason. Stop all forms of sugar and even milk and get a well rouonded multivitamin. See my blog "oxygen, the spark of life".

Paper bag and calm: Suggest that he breathes from and into a paper bag. This will alleviate the effects of hyperventilation. Also try to make the child understand that it is best if he just waits as calmly as he can the feelings will be over sooner. Try to diminish rather than increase to the child the seriousness of the problem.