Answer? Stop thinking.
Counter intuitive hey?
Most of my answers come from being interested and listening, really listening. It took practice to stop thinking and get the answers right all the time. I still sometimes have to pause just to phrase something the right way, but it's getting less and less often. When you have to think about what to say, you are actually filtering the content of your speech through your opinions and thoughts, which pollutes it greatly with lots of garbage that doesn't need to be said.
I've found that it's better impact to say what needs to be said without all the guff of making sure it's the right thing to be said. You come across to people as more honest and forthright, and you become a really good conversationalist. The only downside is that you will have a really good conversation with someone and not remember a word about it because you weren't thinking the whole time. The upside, you will remember the important bits and leave a lasting impact on the other person. Your conversations will also revolve around causing things to happen rather than just talking about stuff.
Once you stop thinking while talking, you become a natural talker. From then it's just like your mind trains itself, while silent, to be better at talking without thinking. What you really want to say comes out instead, and it's far better than the thought created garbage from before. You will however have to stop bending the truth(ieg: lying), as that is purely thought and has no place in honest communication.
There may be some awkward time when you put your foot in your mouth, but actually, you are training yourself to do this less often. In fact, less thinking about what I'm saying means I do this less than before.
The only way to train yourself in not thinking is to listen intently to what the other person is saying. Try and listen also, not just to their words, but also their meaning and intent behind them. There are so many hidden secrets in the way people communicate that are missed when we are busy thinking about what to say, and it's almost like finding gold when you can honestly listen to someone and have a real conversation. Thought conversations aren't real, and after you have the first real connecting talk with someone, you won't want to go back.
So Poker, does this help?
ps. This post took me 9 minutes to write. I only corrected mistakes.