Get to high ground and do not hang out under loose rock or sandstone arches that may crumble with moisture. If you find shelter make sure it is stable and away from water courses. Always carry rain gear even if the sky is blue and the forecast calls for the driest of days. Space blankets are a real life saver. During summer storms the temperature will drop as much as fifty degrees.
Hail can be extremely dangerous both as projectiles and as a cause of hypothermia.
Some hail falls like small wet snowballs and sticks to you like frozen glue. A flash flood can come from a storm you don't even see, so do not linger unnecessarily in deep canyons or in a wash without paying strict attention. If the water in the wash suddenly becomes muddy, get out of the bottom and up onto the wall of the canyon. Drop your bike and climb up if you sense immediate trouble. In the Moab area loose a couple of folks every year or so to lightning.