A theological essay attempts to explore or answer a question concerning theology or doctrine. A theological essay might engage the writings of theologians from different eras, traditions, or creeds on a given subject. It might include subjects like a historical overview of a doctrine, a profile of a theologian's work on a topic, or an argument for a theological perspective in today's culture.
A theological essay might also focus on a practical application of doctrine or theology in a pastoral setting.
Resources that might be useful for a theological essay include (but are not limited to) the Catechism, Code of Canon Law, the writings of the church fathers and other theologians, works in systematic theology and ecclesiology, official church documents, and many others.
Always follow the guidelines for course papers provided by your instructor.
Biblical exegesis is the activity of understanding a passage in its original context and interpreting both the historical and contemporary theological significance of that passage for the journey of faith.
Biblical exegesis requires the use of certain types of resources, such as annotated bibles, lexicons, theological dictionaries, concordances, commentaries, and more.
Quality Research Papers (listed at the right) has an excellent explanation of the exegetical process. Here is a list of the steps in that process, as described by Vyhmeister. For more detail and resources to help you along the way, see Chapter 2 of this text.
Always follow the guidelines for course papers provided by your instructor.
Writing Theology Well by 
Quality Research Papers for Students of Religion and Theology, 3rd Ed. by 
The Seminary Student Writes by 
The Elements of Biblical Exegesis by 
From Topic to Thesis: A Guide to Theological Research by 
Research Strategies: Finding Your Way Through the Information Fog by