When assigning an essay, professors often give a broad topic for students to write about. There are multiple ideas beneath these broad topics, however, and the challenge is choosing what applies to you and your class. For a few minutes, map out the ideas that come to your mind as you think about the topic. From this list of ideas, pick one that seems closest to writing itself. This indicates your high level of interest in the subject matter and will make your writing appear more natural.
Some students may feel that writing an essay is a standardized process -- from composing the initial outline to writing the introduction and finalizing the conclusion. This is not a requirement for receiving a good grade, however. Professors agree that writing what's "ready to be written" allows for the inherent ideas of the student to really shine through. This process not only makes it easier to write, but also generates more substantial content, which can always be edited and rearranged in later revisions for flow.
Tackling too many ideas at once is a common pitfall for students when writing university essays. Faced with the more complex subject matter of a college course, students are much more susceptible to overthink a paragraph, adding in multiple ideas that can end up contradicting one another. Stick to one topic per paragraph, state it in the topic sentence, support all related claims with relevant evidence and cleanly explain your idea. If you feel that you're digressing from the original point, create a new paragraph and start that idea there.
Allot enough time to revise your essay on the paragraph level. Read through and between each paragraph, ensuring that each sentence is structured correctly and that the transitional elements allow for a good flow of the overall essay. Repeat this process with a fresh eye -- you may spot things that you initially missed.
Fundamentally, essays are explanations of your thought processes, ability to defend arguments, and education. Therefore, reading your writing out loud and explaining your essay can determine whether it is well-written or not. Talk to others or to yourself; if the essay is structured well, the explanation of the central theme will be clear to the point that other people can understand the idea just from listening to it.