Don’t be thinking about how to interrupt and make your point; absorb that person’s point first.
Keep your mind open. Smart people don’t win arguments; they gain insight. Let your argument go.
Acknowledge points made by others. Absorb those points. Get them. Get them before you try to counter them.
Understand counter examples. If somebody says trees lose their leaves in the fall then pine trees are a counter example. Counter examples can narrow or disprove a point. The can be logically significant.
Understand analogies. One of my favorites is “paying somebody to write a business plan is like paying somebody to exercise for you.” Analogies can shed light on a subject. They can also be off target, and not apply.
Question the assumptions. Make them explicit. Ask about underlying or hidden assumptions. Help to get people into the right context. Question them if that’s appropriate.
Never be shy about asking what you don’t know. “I’m sorry, I don’t know that term” makes you smart, not dumb. Lots of businesses develop their own insider acronyms and forget that nobody else knows what it means. Don’t assume that the term you don’t know is a commonplace term and you should have known it.
Change your mind sometimes. Often. Smart people listen, think, acknowledge, and, learn. They have open minds. And open minds will change when they absorb new ideas and new angles. Changing your mind makes you smarter.