What is the best and most effective way to handle a very demanding guest?

Patience and Professionalism. Worked in a call center before and handled I-Rate customers, the only way to survive the day is being patient and stick to company conduct of bringing best and polite service to the customer.

Patience is our only tool and defense with demanding customers. 

No doubt patience is very important in all aspects of matters but selection of words in dealing with demanding customers have most of importance too.