The literature essay prompt usually appears on advanced composition and writing skills tests, and asks students to explain and respond to one or more pieces of writing, often an essay and a poem side-by-side. Since the literature essay is a broad category that describes the thing being studied (literature) more than it describes a particular method of composition, it often requires knowledge of other essay types, especially the critical, comparison, and analytical essay. If you're studying to take an in-class literature or composition test, you'll definitely need to become comfortable with the basic five paragraph essay structure.
Since literature essays are assigned to test how well you can understand and explain a written text, their primary focus should be on the use of language within a work of fiction, poetry, or expository prose. Therefore, unless a literature essay prompt specifically asks you to make a generalization about life, it's best to avoid bringing your personal opinion to the text you're explaining. What you need to understand and explain is the author's point of view and how the author's language supports that point of view.
The primary skill required for writing a literature essay is professionally known as "close reading." If you've never heard of it, that's not surprising, since close reading usually isn't referred to by name in college classrooms today. The term came to prominence in the mid-Twentieth Century, and essentially means reading to understand many levels of meaning within a given text. Here's how close reading impacts you: although it's currently unfashionable to teach close reading as such, professors still judge and grade literature essays based on how well students are able to understand both the literal and figurative meanings of what they read.
Preparing to write a literature essay well, then, means becoming familiar with the critical terms implied by the unspoken but still operative close-reading approach to composition. Understanding character, irony, theme, metaphor, and simile is a good starting point, and most composition classes at least begin to discuss these concepts.