This assumes that you know the material, that you have the information to put into the essay. It helps if you have studied for the exam by anticipating possible essay questions, thinking about the general patterns in the material instead of just aimlessly memorizing.
Analyzing the question is at least half of writing an acceptable answer. Therefore, first read the entire examination; this avoids overlapping answers and a detail in one question may jog your memory about another question. Many questions are written so that they contain in themselves an organization you can use for your answer; if you follow this organization your information will automatically be relevant. By borrowing the organization of a question, you will find it easier to select concrete details and facts with which to support your answers; one of the things a teacher looks for when grading is supporting material-facts-for your generalization.
If the questions have different values, divide your time accordingly, either with regard to time limits given or by the number of points per questions. Be sure to follow your time schedule rigorously; this will help you avoid coming to the end of the test period with one or two questions left to answer. Also, if at all possible, save time to re-read your answers.
After scanning the whole exam and setting time limits, read each question closely before writing your answer. You must decide what kind of answer is expected and, to help you, in most questions there is at least one key word. The verb of the question is often the key word to the type of answer expected.