You change the whole essay - in class you should have studied enough points to fill a few essays and done some practice questions.
You need to go in with a very good knowledge of the texts - do practice essays but don't learn any. Once you get into the exam, try not to stress - read the question, circle and highlight the question words (identify, etc.) and key words (main words in the question).
Yes, change your thesis - a thesis is basically your idea or hypothesis (answer) to the question. So, to give an example you will surely understand (as we probably haven't done the same texts):
How does Shakespeare show female characters with respect to his context?
This question is asking you to explain, and the key words are 'with respect to.'
You may wish (depending on what year you're in) to use your introduction to explain the value of women in Elizabethan society. (The play I will use is Macbeth so you may want to read a very quick summary.)
Your introduction is a summary of what you are about to argue - it sets up the basis for your essay, maintaining references to the question - if two questions are different, the introductions used to answer them cannot possibly be the same, nor can the theses used to write the essays!
Intro: women were not seen as equal in shakespeare's society and were often thought to lack intelligence, however Shakespeare was inspired by Queen Elizabeth's power and intelligence to write several plays, such as Macbeth featuring very strong female characters, both physically and mentally. He shows the influence of Lady Macbeth on her society in a time when women were seen to be inferior.
This would be my essay plan - ALWAYS PLAN!
Paragraph 1: Lady Macbeth is depicted as evil ("Come thick night and pall thee in the dunnest smoke of hell, that my keen knife see not the wound it makes.")
Paragraph 2: Lady Macbeth's instigation of Macbeth's downfall.
etc. Learn quotes relevant to the themes you have studied and maybe some that others won't have as well - these fetch marks.
Use your conclusion to re-iterate your argument and prove to the marker that you answered the question.
Hope that helps - I wasn't sure if you wanted general essay help - the main thing is that THE FIRST THING THE MARKERS LOOK FOR IS WHETHER THE ESSAY ANSWERS THE QUESTION.