Thinking critically is an important part of being analytical, and asking questions is the first step in being critical. You should question the information that is provided to you. If something is not necessarily a fact, it is a statement from someone else's opinion. You need to question the reasoning behind the statement. You can even question the reasoning behind your own reactions to the information you are evaluating. If you are upset or in strong agreement with the prompt you are reading, ask yourself why you feel that way. The answers to your questions will lend to an interesting argument for your paper.
Discussing your topic with the whole class is a common analytical tool that teachers use in the classroom. This practice can provide various perspectives from the other students, which can help you open new doors of interpreting your information. Other students may understand the information differently than you, and see points that you could not see on your own. These discussions can either alter your own point of view or strengthen your original assertion.
Be objective when you are evaluating information and consider the source. Every writer has an opinion about what he is writing, even if he tries to hide it. The point of view of the information provided to you can alter the interpretation of the facts. There are always two sides to an argument, and each side is going to claim to be right and innocent. You should certainly come to your own decision by the end of your evaluation, but while you are assessing your material, try to be as unbiased as possible. Do not come up with your own opinion until you have tried understanding all sides of the information given. If you are too judgmental initially, you may miss some vital information that could make holes in your own argument later on in your essay.