In addition to writing essays and having them reviewed, I highly recommend reading over as many of the model answers to previous essays as time permits. Quite a few are provided for free at the link below and more recent essays can be purchased on the NCBE website.
Further, a bit of guidance is provided on the test itself as to how you should aim to style your answer. On the MEE, there will be the following instructions:
Demonstrate your ability to reason and analyze. Each of your answers should show an understanding of the facts, a recognition of the issues included, a knowledge of the applicable principles of law, and the reasoning by which you arrive at your conclusions. The value of your answer depends not as much upon your conclusions as upon the presence and quality of the elements mentioned above.
Clarity and conciseness are important, but make your answer complete. Do not volunteer irrelevant or immaterial information.
Answer all questions according to generally accepted fundamental legal principles unless your testing jurisdiction has instructed you to answer according to local case or statutory law.