Small planes fly from Albrook (Marcos A. Gelabert) Airport in Panama City to Contadora's small airstrip several times daily. The journey takes about 30 minutes and is operated by Air Panama and smaller charter services. This is the most practical option.
A passenger ferry also runs from the Causeway (Amador) in Panama City, though the journey takes several hours and service is less frequent. Check current schedules before planning around it.