To write an assignment concerning a succession planning process, you need to choose a company for which to write a plan. Consult your assignment sheet or teacher to see if ylou should use a fictional company (perhaps a fictional case study company you used in class?) or a real company.
Whichever you choose, you need to examine succession planning not simply as choosing a successor for one CEO, but thinking about how promotion, training and mentoring processes can serve in an ongoing fashion to groom employees for all positions likely to need successors in the next 5 to 10 years. For example, rising young stars may need to be cycled through multiple areas of responsibility (finance, marketing, product development, international posts) to gain the knowledge necessary for executive rank. Therefore you should make succession part of an overall HR strategy on all levels rather than a singular event.