To get a high score on the analytical section of the GRE, it's crucial to understand the difference between the two essay prompts you'll see. The "Analyze an Issue" task requires you to persuade your reader to accept your perspective. The "Analyze an Argument" task requires you to evaluate the logic of someone else's argument. The Educational Testing Service publishes scoring criteria for each task and for the analytical writing section as a whole. Read through the criteria carefully, and look at the sample essays and the scorer comments that accompany them.
Each task will have one of several possible instructions, which are listed on the ETS website. For example, a possible prompt for the argument task reads, "Write a response in which you discuss what specific evidence is needed to evaluate the argument and explain how the evidence would weaken or strengthen the argument." Review all these prompts ahead of time and make sure you understand what each one asks you to do. You'll save time on the test if you can just glance at the instructions, rather than having to interpret them then and there. On test day, be sure to account for all portions of the question -- for instance, the example above tells you both what your main points should focus on and what kind of rationale you must provide.
Both portions of the analytical writing section require you to take a clear position and to present specific evidence that supports your claim. Much of the scoring depends on your abilities to make a claim about the issue or the argument's logic, to offer main points for your claim supported by reasons and examples, and to connect your ideas logically. Consider creating a brief outline of your main claim and main points once you read the prompt, but before you start writing, since mapping out your answer will give you a better sense for where to insert transitions and evidence in your essay. Try to provide more than one reason or example to support each main point you make.
Once you understand the expectations and parameters for the analytical writing section, nothing will improve your score more than practice will. The ETS website actually includes all of the possible issue prompts and argument prompts that you could see on the GRE, along with instructions for each one. The only difference is that on test day, the GRE might pair each prompt with different instructions than the website does. Because there are so many possible prompts, you're relatively unlikely to get tested on one that you've practiced, but your facility with both tasks will increase with even a few practice essays. If possible, have an instructor or writing center staff member at your school look over your answers and discuss how you could make them stronger.