How do I execute an essay question successfully under exam conditions?

First of all, planning is everything. You should spend at least five minutes reading through all the essay questions you are presented with assessing each one with careful thought and consideration and asking yourself what exactly each question is asking you to do. Is it an discursive essay? Are they asking you to argue for and against a statement? The rhetoric used in the question itself is of paramount importance. 
Secondly, don’t be overwhelmed by the questions. Take a breath and pick one you feel you can attack the best, highlight the key words and set to work on a plan. Make sure you understand the question and what it is specifically asking you to do; is it to be answered using one text or various? Are you going to be repeating information that you have used in previous coursework or in another portion of the exam? This is always asked to be avoided as they want to see what range of ideas you have. 
Planning: the most important part of your exam! It’s always very tempting to regurgitate all the information that you have taken the time and effort to memorise but actually isn’t relevant and, as bitter a pill that is to swallow, it’s something we just have to accept. Make sure your content is original (as in, not copied directly from a textbook) and appropriate…you may think your point is valid and original, but if it doesn’t pertain wholly to the essay in hand, the superfluous information will work against you, no matter how groundbreaking the idea may be. 
Work with the idea of a hot air balloon analogy in mind. The introduction is your balloon, the place where your ideas begin. The ropes that hold the balloon are your paragraphs, ideas and examples that stitch the essay together, and stem from your big balloon ideas. The basket is your conclusion, which ties everything together to create a full, well rounded and well thought through piece of work.