Pause and think before you reply, even if you know what you are going to say. It suggests that you respect the questioner and it will reduce the chances of conflict.
Repeat the main points for all but the simplest questions, to show that you have heard and to ensure that you are dealing with the questioner's real concerns.
Give the most direct answer that you can in the opening sentence. We are so used to watching politicians dodge the issue that we rarely start an answer with 'yes', 'no' or 'by 23 October', even when this is the point we want to make.
Use stories or anecdotes to illustrate your answer. But make sure you explain why they are relevant.
Repeat your one-line answer before finishing - research suggests that people are more likely to remember the first and last things they hear.
Check that your questioner believes the question has been answered before moving on - this gives you another chance if you've missed the main issue.
Build the question into something challenging if it is unclear. To make the questioner more sympathetic, you need to make them feel cleverer than they are.
Make eye contact when the questioner is speaking and at the beginning and end of your answer, but not the whole way through, especially if there is an audience; they will want to feel that you are talking to them as well.
Prepare answers. Think about all the tricky questions that you might be asked beforehand. Try these out on a colleague, or at least say them out loud - you will quickly spot what sounds impressive and what does not.