Begin by exploring ideas through a freewrite. This means writing without stopping or editing yourself for a set period of time. Don't be afraid to change your train of thought in the freewrite; the purpose of freewriting is to generate and explore new ideas, even if they seem disconnected at first. Write about what intrigues you. Through this unselfconscious process, you'll come to better understand what you think about a topic.
By connecting less accessible ideas like scientific concepts to your own experiences, you'll make these ideas more palatable to readers. Strong narrative writing often displays connections between seemingly unlike ideas. Not only does it make technical ideas easier to understand, it creates a rich and interesting blend of associations. After freewriting, try making a rough flowchart of the different related ideas you're exploring, to give yourself an accessible visual to work with.
As an old writers' maxim says, write what you know. Write what you feel passionate about and have personal experience with, whether it's a place or an activity, and include details that only an expert would know. Details that at first seem mundane or commonsense might spark the interest of a reader who has no background in the subject, so tell stories to your friends to find out what intrigues them. And remember that even if the topic is painful, writing can be cathartic, helping you to release negative emotions while helping others who are experiencing something similar.
Dialogue can liven up an essay when written well, though many people don't associate it with the essay form. Hone your skill at writing dialogue by listening to how people talk in different settings. Listen to people in a café, and take notes. In your essay, if dialogue fits the style, chisel it down to leave out excess words and show the personality of each character who speaks.
As WriteExpress suggests, have other people read your essay after you've revised your first draft. Ask them to be honest and single out anything confusing, or any intriguing points they'd like to know more about, as well as other rough patches. You don't have to take every piece of advice you're given, but if different people consistently give you the same advice, you should probably use it.
As Nancy Atlee says in her book "The Absolutely Essential Writing Guide," the structure of narrative essays is flexible and style options are varied. Read the works of many different authors to gain a sampling of the many possible styles to use in your writing. Though your voice will, hopefully, be different than that of any other author, this will help you to explore the direction in which you want your writing to go.