"The four functions of management in a health care setting are planning, leading, organizing, and controlling. These functions provide the basis for the common model used in most health care management training programs." What would be examples of these functions?

Healthcare management requires a number of functions. These four main concepts serve to direct the healthcare organization and enables them to properly succeed at treating patients.
Planning is the first step in any process. An example of planning would be resource planning—setting up an account of how many beds are needed, as well as doctors and nurses, in addition to all of the medical supplies. Properly ensuring that the correct amount of supplies are on hand allows the organization to be prepared in any situation.
Leading is just as vital for healthcare management as the other functions. Because of the stress and confusion that is inherent in the healthcare industry, leadership is required to direct the staff to the correct actions and solutions. For example, when there is a rush of emergency medical needs, a manager will have to organize their doctors and nurses to be able to handle the most individuals in the most efficient way possible.
Organizing is another vital component. Without organization, the resources that have been so carefully planned may never get properly used. An example of organization is having the medicine laid out in a contained and yet easily sorted manner.
Finally, controlling deals with ensuring that everything is up to the highest levels of safety and quality. Controlling the organization includes ensuring that it is kept organized and maintained properly so that it will maintain certification for safety standards.

Planning, leading, organizing, and controlling are the four key elements of any management process, and the health-care setting is no different. For the purposes of this answer, I will apply these elements to the environment of a hospital, as this is where most health-care management training programs take place.
Planning, in the context of a hospital, is about looking to the future and analyzing new medicinal techniques that are becoming available. The purpose of this planning is to make sure that the hospital is still taking as good of care of its patients in the future as it is now.
Leading is about being a decision-maker and providing a voice of authority that all doctors, nurses and other personnel listen to. Management needs to listen to the concerns of the medical professionals, because it is only by listening to their needs that the needs of patients will be met.
Organizing is about making sure that the current needs of the hospital and its staff are being met. Have the staff lists been done? Are the medicine stocks high enough? Are emergency protocols in place? These are the types of questions that hospital management needs to ask in their role as organizer.
Controlling, in the context of a hospital, is about ensuring that everybody is doing their job and that everything is being done according to accepted protocols. Controlling involves investigating any allegations of malpractice or negligence that arise and ensuring the overall smooth running of the hospital.

1) Planning: Planning requires engaging in environmental scanning, or understanding the conditions of the organization, combined with setting long-term goals and/ or short-term objectives for the organization to meet based on these conditions and making plans for how to meet those goals. Whether working in a for-profit or non-profit setting, planning is needed to make sure the future of the organization remains bright. A good planner in the healthcare environment knows which areas it is most important to look ahead in. In the healthcare setting, goals could be created for better information systems, patient care, or office management—all of which should lead to greater efficiency, greater productivity, better optics/ PR, and ultimately more profits or funding.
2) Leading: Healthcare is a difficult profession, and medical professionals working in a managed setting need good leadership and guidance. Doctors need to be able to trust their needs will be met and that concerns about things like equipment, staff, or scheduling will be heard. It is absolutely critical for nurses and techs to feel heard and well-led in this setting, as they often feel overlooked. Having a strong and understanding leader guiding the "lower-level" employees will ensure they remain committed and attentive to their jobs. A good leader is one who will help make the long hours and difficult cases worth it.
3) Organizing: An organizer needs to be able to design their setting so their plans can be carried out properly. In healthcare management, this could include things like developing new jobs, redesigning current jobs to improve vertical integration, or increasing or reducing specialization of job assignments to improve productivity within departments. 
4) Controlling: Almost nothing is more important in healthcare than making and meeting standards. Standards are absolutely critical for the safety of both the staff and the patients. An effective healthcare manager must have a very, very strong understanding of both standards of patient care (including front office rapport, bedside manner, effectiveness with social workers) and basic standards of medicine itself, such as being able to understand if lab techs are getting sloppy or if a doctor is making a number of misdiagnoses.