The best writers may be born, not made. But all writers can improve the way they write. Like many craft skills, the ability to write well takes a long time to develop (practically, it may go on developing for a lifetime), and it is more a matter of learning than teaching. Teachers can't teach you how to write; you can learn, and teachers can help you to learn.
However, if you are searching for guidance and getting started, you may like to look at some simple principles.
All good writing is original - that is, it is different, so you must find your own 'voice'.
Good writers think about their readers. So a student writer should think about the teacher who is reading the assignment. If you can write in a way that your teacher likes, you will on the whole do better.
All good writers think about why they are writing - be clear about why you are writing, and you will write more clearly.
Be aware of the temptation to show off - to write things in as ornate or florid a way as you can. Dr Johnson once advised a writer: "Read over your compositions, and where ever you meet with a passage which you think is particularly fine, strike it out." (In Boswell's Life of Samuel Johnson (1791), entry for 30 April 1773.)
Student writers should be aiming to write like professionals in their subject - which, after all, is one purpose for which they are taking a degree course. Further tips directly for students writing for the purposes of Higher Education, including those thinking of applying, are at Good academic writing.