In real life

1. Listen to what people are trying to say, properly.
2. Before you say anything, take a short pause; and slow down the delivery of your words.
3. As you talk, think about what the other person doesn't know, and how you can make them know what you know; adapting the words you say, so that they understand you.
4. Use a clear structure when explaining things, so people will know what your point is, while you're talking.
5. If you aim to express your thoughts on the situation, make them short and sweet, succinct, so although your opinion is expressed, what you're saying is more about facts, than it is is about your opinion.
6. For explaining things to an audience, make sure that everything you say is for a reason.



On Quora

Answering on Quora is much different to explaining things to people in real life, so this may not help you.

Use Quora more often to answer questions of which you can explain things, that nobody else knows the answer you want to explain.
Browse your favourite people's Quora answers, and see how they explain elaborate things. You should also read. Which Quora users have the most distinct, recognizable writing styles (for both questions and answers)?