What are good ways to help a panic attack the moment it's happening without therapy or drugs?

Breathing, relaxat'n. General idea is to create a state incompatible with panic. Deep, slow breathing is a good strategy, and sometimes breathing in/out of a paper bag can break a cycle of hyperventilation, which can cause panic. Muscle relaxation techniques often help, eg, learning to tense then relax muscles ("progressive relaxation"). Finally, have a peaceful image ready to bring to mind when panic strikes.
What do you mean? Panic attacks can respond to simple things like deep breathing or taking your mind away from the actual panic attack. One easy way to get your mind away from it is to squeeze your toes really hard until they get tired or painful. That will veer your mind away from the anxiety to the pain or fatigue. However, beware that these are all considered "therapy" techniques.