I think that the previous post did a good job in identifying how to go about this particular task. I would say that it might be helpful for you to investigate some of the resources that talk about what it is like for kids to learn in a classroom environment where they have power. I think that this might be a very interesting aspect of the argument to develop. If classroom prefects and monitors are elected by the students, students have a better chance to feel as if they have power in the classroom setting. The research pans out to state that this feeling helps them do better in school and studies because they feel their voice is validated. Certainly, this would be so if they could elect their student leaders, for they would feel a certain level of empowerment and control of the classroom setting, where power can emerge from "bottom up" as opposed to strictly "top down."
If you have to determine your position on an issue, you first have to make a list of the advantages and disadvantages of both elected and appointed leaders. This is the basis for the main points of argument/persuasion in your essay.
Once you've determined your position, write a strong statement of purpose which outlines the key points you'll be discussing. For example: Prefects and class monitors should be elected because....
I assume you have some personal experiences to use as examples and specifics for each of your main arguments. (Has anyone ever abused his/her power when appointed? Have you been more willing to follow if you got to help choose the leader?) Use some kind of specific example, personal or not, to support each point of your argument.
Finally, summarize your position in a strong conclusion. The most effective introductions and conclusions are somehow connected (think about coming around full circle, referring to or finishing something in the intro when writing your conclusion). Your readers want to be intrigued by the intro (give them a reason to continue reading) and satisfied by the conclusion (don't just leave them hanging).
This is an interesting topic, and I'm confident you'll find plenty to say once you sit down to make your list. Good luck!