How is coffee decaffeinated?

The Swiss Water Decaf Method 

To prepare the coffee beans for decaffeination, the beans are pre-soaked to rehydrate to a target moisture level that is ideal for caffeine removal.  This step also cleans the beans from dirt, dust and silverskin. Caffeine is then removed from the beans through a carbon filter system. 

Green Coffee Extract, (which is made out of fresh water and all of the soluble solids except for the caffeine) is circulated around the green coffee until there is less than .01% of caffeine remaining.  This process takes about 8-10 hours.  

The result, is that your typical cup of coffee will have just 2 mg of caffeine as compared to 95 mg in regular coffee!