This basic skill is central to getting good grades in college.
Perhaps you will get an instructor who will accept a rough approximation of the assignment. Don't count on it. You should treat the assignment as if it were cast in concrete: every detail, large and small, is vital and non-negotiable. If you have trouble with some particular, discuss it with the instructor before the due date. Don't assume that you can simply do something different and turn it in on your own schedule. If you're lucky, that strategy will earn you a low "C". If you're not so lucky, the teacher might not accept the paper at all.
You would be amazed how many students think they can write a major essay without actually reading the assignment sheet. They might hear ("listen to" is the wrong term here) a discussion of the paper in class, then pick up a few key words and ad lib from there. One of my students was supposed to explain a key characteristic of the University in an article for a popular magazine. She only picked up the word "magazine" and wrote a movie review instead. Another was assigned to write a comparison of two discussions of the First Amendment. He saw only the word "compare" and submitted a comparison of Kobe Bryant and Lebron James. Both of those papers failed to do any of the work they were asked to do.
Instructors often give you a choice of topic. That's because some writing assignments simply leave a person cold—and the ones that leave you cold might really excite your neighbor. Choose one of those assignments, and only one. If you get an assignment sheet that says, "Choose one of these for your paper," do not cram all of them into the same essay! You will probably end up with a piece that is shallow (because it only gives part of a page to each), has no unity, and reads like a quickie catalog page. That's not the path to a good grade.
Professors have a tendency to write like professors. University vocabulary is their native language. If you don't know the definition of germane or ancillary, look it up! Do not assume that people who use big words are stupider than you are. Do not assume that the big words are somehow unimportant. And don't get insulted if the professor used a word you don't understand. (After all, you did come here to learn something, didn't you?)
Some assignment sheets are long and complicated, including examples and hints for success. Buried somewhere in the good ones (I am crossing my fingers on this one) will be a command: "Write an essay that does X."
Some assignments are phrased as a question or a series of questions. Think of your paper as an extended answer. If you get several questions, you are not expected to produce a set of bullet-point answers; you are expected to come up with a single smart something to say that deals with the questions. (Students sometimes say, "I answered all the questions. Why did I get a poor grade?" They got a poor grade because they didn't provide an essay that had a unified vision and a thesis that communicated it. They only answered questions; they thought they were taking a short-answer test.)
Most assignments are more specific than "write about X." They will use words such as explain, illustrate, narrate, compare, contrast, discuss, defend, or analyze. Each one is a particular task, and you must become aware of the distinctions between them. If you are asked to defend a point, but you only define it, you haven't done what was asked for (and your grade will probably suffer badly).
Is this supposed to be MLA format? Does it include a bibliography? Is it paragraphs or a numbered list? Special requirements often are related to special goals of the teacher, so don't assume they are foolish or unimportant, or that the teacher won't notice. (A colleague who teaches math tells me that he wants homework submitted on graph paper. He says he cannot understand why students will accept a five-point deduction time after time rather than using the right kind of paper.)
Many of my students are unable to write the prescribed length of paper and unwilling to ask for help. Because the University has a Writing Center and professors have office hours, "I couldn't think of anything else to write" will not work as an excuse. Anyone who has taught more than one course has seen all the immature tricks to fake a longer paper (wide margins, large type, etc.), so don't try them. Your instructor will probably be insulted because you thought such a pathetic antic would work. (By the way, for papers submitted through Blackboard, these tricks are pointless because the teacher can easily get a word count.)
Are there intermediate due dates (rough drafts, outlines, and the like)? Assume that every due date is a non-negotiable, absolute requirement. Set up a personal writing schedule so you can hit the final deadline(s).
Unless the assignment specifies otherwise, you should assume that your audience is your instructor, who has written this assignment with certain goals in mind. A secondary audience is a group of your peers, young adults much like yourself. Knowing this, you know several things: