How do you control the use of smart phones in an organization?

It depends whether phone given by company or his own. If the phone given by company then IT dept. can restrict most of things. Firstly you can provide single SIM phone and SIM should provided by company. If you stop internet data from SIM then user can not connect with internet and this is the main solution of reduce of phone use. If company providing wi-fi then make policy on your firewall and allow users data according to their use. 

If the smartphone is employees own then it is very difficult to monitor it. 

Nowadays, most employees rely on their smart phones for an easy access to business related documents while they're travelling. However, it is extended even when inside the company premises. I do notice that most of the time because a smart phone is like a portable computer. But to limit the use of smart phone inside the office: first it must be agreed upon all the staff  that smart phones are prohibited during working hours and be implemented and written on the employee handbook or personnel policy otherwise such punishment or warning will be imposed. Inform the IT department to remove all mobile devices connected to WiFi but make sure all staff has a properly working laptop or desktop and telephones. You can also implement a minute phone break. Normally such rules are implemented in call centers.