Travel east on Hwy-9 toward Mt. Carmel Junction. Pass through the long 1.1 mile tunnel and then through the small tunnel. Eastbound the road will make a turn right then a long sweeping horseshoe turn to the left. Immediately on your left is a pullout for parking or a little further down the road there is parking on the wide turn directly across from Cockeye Falls.
Follow the obvious path down into Clear Creek. Use the plentiful shelf system to work higher onto the hillside of the opposite side hiking back toward the falls. You should reach the top of the falls as you reach the top of the shelf system.
Caution needs to be used while crossing Clear Creek, if there is water, it will be difficult to cross and perhaps you may not want to, Clear Creek is a major tributary for run off on the East side of Zion and should be avoided if rain is in the area.