The opportunity for you to ask a question often comes only at the end of the interview. In fact, you are typically offered the chance when the interview is over: "Are there any questions that I can answer for you?" However, there is a question you should ask of every interviewer as early as possible during the course of the interview: "Can you tell me about the position and the type of person you are seeking?"
Properly positioned, this question can provide you with your single greatest opportunity for understanding more about the job and your ability to fill the role. The answer can show you the specific areas of need you should address during the course of the interview. So it is important to inject this question into the interview as early as possible. You can do this with an out-take question. As you finish an answer, use it as a lead to your question. Be careful not to use this technique as an attempt to control the interview. You merely need to use this technique to inject this critical question.
For example, in answering a "What do you know about our company?" question, you can answer directly with what you know about the company (you have done your research, right?), then state that you do not know as much about the specific position. Turn your answer into the out-take question: "Can you tell me more about the position and the type of person you are seeking?"
Find the strategic opportunity to inject this question as early as possible in the process. Then, as appropriate, frame your answers around what they are seeking in the person to fill the position. Stay within practical bounds in directing your answers, yet keep in mind the perspective of the interviewer and seek to meet their needs for the position. You will be further ahead in the interview than if you merely take shots in the dark, hoping for your answers to magically hit the mark.