Listen to people's conversations and observe how people talk to each other. This helps you to gain a better understanding of how conversations flow.
Write like you're talking to a friend. When you focus on explaining your essay to one person instead of an infinite number of people, it helps you avoid writing a speech or anticipate everyone's reaction. Also, you write as though you're talking directly to the reader.
Show, don't tell. One way to engage your reader is to use active rather than passive writing. Active sentences allow you to get straight to the point.
Edit your work while you're writing and after you complete the piece. Eliminate needless words. For example, in the sentence, "The oak tree fell against car as I stood and watched." becomes "I watched the oak tree hit the car."
Write as though the reader has no prior knowledge of your subject. You want the reader to have a clear understanding of your topic. This helps to incorporate a conversation style into your essay. Thus, when you're revising your work, anticipate the questions your reader may have.
Read your essay out loud after you've finished each draft. Reading aloud allows you to ensure you have the conversational style you're trying to convey. For instance, while reading the essay, if you notice that your writing is too wordy or impersonal, you have the chance to revise it.