Writing is a skill, and like any skill — if you want to get better at it — you must practise it. To become a better writer at university, you must find opportunities to practise and not only write when you have to (such as when you have to do an assignment). Your first step in finding opportunities to practise writing is to see what your university offers — they may offer a writing course to complement your subject-specific studies or have an academic skills support service. Next, take any opportunity that your lecturers provide to submit drafts. Submitting a draft means that you are not only writing and getting your initial ideas on the page, but that you will receive feedback to help you revise and improve your work.
Other opportunities to practise writing at university may also be available — you could write for the student newspaper or write a blog for a student society. Keeping a daily journal is also a good idea and will help you get into the habit of consistent writing practise whilst providing an opportunity for you to explore ideas that may help with your studies.
The more you practise writing, the more automatic parts of the writing process will become for you. For instance, as your typing improves, you will be able to focus more on making sure your writing says what you mean and less on the physical act of typing. As your writing continues to develop, you will be able to focus more on the reader and ensure that your work is as easy as possible for them to read and interpret. And you never know, you may start to enjoy it!