Complete any GRE study guide that you choose from a bookstore or library. Go through the study guide in great detail and understand the rules of the exam.
Read the two essay questions at least three or more times when you sit for the GRE.
Write a complete thesis statement that addresses the question. While this seems obvious, many people do not write proper thesis statements, and this sets the tone for your essay and your score.
Take the issues from your thesis statement and expand on them, step by step, throughout your essay. Use specific examples to back up your points.
Be methodical when writing your analysis; you do not need to be creative here--you do need to be thorough.
Include analysis, not just explanation. For instance, "The French aided the colonies in the fight against the British because the French were longtime enemies of the British crown" is an explanation. "The French aided the colonies in the fight against the British not merely out of a sense of revenge against the British crown, but to gain direct access to raw materials exported by the colonists, which would give France an economic advantage" is analysis.
Put your thesis statement in context. If your essay is on the French and their involvement in the American Revolution, for instance, mention how France's involvement affected European politics.
Write a conclusion that restates your original thesis and discusses how you've addressed the thesis points.
Carefully reread your essays and clean up any spelling errors, grammar errors, etc. Make sure you've touched on all the major areas in the essay question.