Think of the acronym TAP. T. stands for Take Time and develop Self-Trust A. is for Audience and P is for Practice.
(The steps below should be used when you believe you know how to respond to a questioner. They should not be used to bluff your way out of a difficult situation. When you clearly do not know an answer, admit it.)
Firstly I'll elaborate on the T. that is, Take Time and develop Self-Trust. When you're put on the spot and someone asks you a difficult question, take time. This means you should take time by drawing in a breath much more slowly than you normally would. A slow breath can take up to two seconds and you can use that time to organise your thoughts.
Take time by initially speaking at a moderately slow speed. When you gain more confidence you can speed up. Take time by slowing down your body movements and gestures. If you're seated and are required to stand prior to responding, move from a seated to a standing position slowly.
These techniques will calm your mind and better allow you to access the information you need.
Develop self-Trust means to use positive self-talk in the moment to encourage your mind to find the ideas. One useful phrase to say silently to yourself is 'YOU CAN DO THIS'.
The A. in TAP is for 'Audience'. Use the Audience as appropriate to the situation. You can ask the person who asks a question to repeat the question. You can use part or the entire question in your answer.
For example, If someone asked me, "Tell me what causes stuttering?" I could answer, "Max, the answer to what causes stuttering is not well understood. However . . .etc"
You can also have a member of the audience answer the question before you do. When someone asks a question of you, simply say, "Before I respond does anyone else have a point of view on this question?" After the other person has responded you can give your answer.
The keys to doing this step is to firstly know if it is appropriate or inappropriate to allow another person to answer a question directed to you. Secondly, widen your field of vision of the audience and look for people who seem keen to respond.
By allowing others to respond you share the power of the front of room or presentation space, and you'll be perceived as more confident and composed by allowing others to give their point of view.
You can also decline to answer a question if it is more appropriately answered at another time in your presentation. If you choose to tell the questioner you'll answer at a later time, make sure you do or you'll lose your credibility. Don't defer answering a question because you don't know the answer. As previously stated if you don't know the answer to a question, admit that you don't know. Then genuinely offer to find out the answer and get back to the person.
The P. in TAP is for Practice. Before an important presentation or meeting have one or two of your colleagues fire questions at you, which you might be asked in the meeting. Use the above techniques as your answer the questions.
Whenever you practice be sure to practice aloud. Your body needs to hear and feel your voice and words and body language in a practice situation in order to give it confidence to respond confidently in a live situation.