Know your audience:
First of all you should know who you are going to address. It is very important to know the mental calibre of your listeners as it will help you to prepare a list of questions that can be asked by the audience.
Listen to the question:
Pay full attention to the person standing in front of you with a question. Listen to the question as it will help you to understand that what they are expecting from you. Most of the speakers begin the answer before the question is even finished. This is really unprofessional and objectionable.
Repeat the question:
Allow yourself and the audience to understand the question by repeating it. It will help you to gather your words to formulate the answer. If you do not want to restate then giving a small pause is also a good idea.
Admire the person:
Encourage the person for asking the question as it will also urge others to ask relevant questions. However, you should say something wise otherwise this can give the impression that other questions were not up to the mark.
You may say something like; I’ve been thinking about that very question a lot lately myself or many people who go deep into this topic ask that question etc.
If you think that you are good to go then start replying to the person. Be confident and definite otherwise your audience may gets irritated. Cover all the aspects of question one by one. It is always better to divide the question in different parts.
You should be honest to yourself and your audience. Do not try to give the impression that you know all. If there is something beyond your knowledge, admit it and promise to get back to them with proper answer.
Do not argue:
If the audience is not satisfied with the answer do not argue. The proper way to move to the next question is saying something like, hope the question is answered.