How to write an essay on moral theology?

Moral theology, a Catholic teaching, is:

A branch of theology, the science of God and Divine things . . . [which] is limited to those doctrines which discuss the relations of man and his free actions to God, and his supernatural end, and propose the means instituted by God for the attainment of that end.

In other words, moral theology is interested in how a person's actions line up with divine intent. It assumes that God has created humans with the free will to make their own choices and that he has provided us with methods and instructions to act in accordance with his will. If morality is a discussion of how actions are determined to be right or wrong and theology is the study of God and his nature, then moral theology is the intersection between divine will and human action. Moral actions would be those that line up with divine will, while immoral actions would be those that deviate from it. 
There are a few approaches you could when writing an essay on moral theology. First, you could summarize and examine what moral theology is and what it teaches (as done above). Second, you could explore figures and teachings in Catholic history that are relevant to the development of moral theology. St. Thomas Aquinas, John Finnis, and the various papal encyclicals that deal with human action would be good sources to investigate. Third, you could look at how Catholic moral theology compares and contrasts to other sets of ethics. Within Christianity, you could compare Catholic morality to Protestant morality, or you could compare it to Buddhist or Islamic ways of thinking. 
The links below can provide further information to help you. Good luck!
http://www.newadvent.org/cathen/14601a.htm

http://www.pathsoflove.com/blog/2010/02/aquinas-moral-theology/

https://www.ethicssage.com/2012/09/the-role-of-ethics-in-religion.html