If you've never written an essay before or if you can getting assignment that forces you to write in the style of essay that you have not encountered, you may be concerned as to whether or not your skills are going to be good enough. After all, you may believe that it is not an easy thing to become a good essay writer. However, most of what can make this particular thing difficult is the way you approach it and what mindset that you have. Indeed, this is one of the main and most important things to think about no matter what the assignment or what you're doing. Your mind ultimately is what will bring you success or failure.
The first tip to consider is that if you've not dealt with a particular style of essay, the best thing to do is to ask your Prof. for some tips or even for a previous example essays for structured formatting. This alone will allow you to quickly see at least in a general way, what the particular essay style entails and needs and will allow you to quickly pick things up and become a good essay writer for that style. Never be afraid to ask questions or ask to see samples especially if you're not entirely sure about the type of essay you have been asked to write.
Something else to consider is that there is really no time limit for becoming a good essay writer. In fact, if you try to rush things you will find that you make more mistakes and have or problems writing coherently than if you were to just relax and simply write. Remember, some of the best writers took years to perfect their craft. As such, you shouldn't expect to become a perfect essay writer with yotr first assignment. It will take some time and it will take several assignments for you find a style and voice that suits you.
If final tip is to understand that a good essay writer does not expect perfection with the first draft. It will most likely take several drafts and rounds of editing for you to get the essay to the point where you feel comfortable handing it in. This is not something that should frustrate you as this part of the writing process in general, no matter what you write.