Stop thinking!
Many people think you have to be a quick thinker to do improvised comedy. Yes, you are able to speed up your thought processing by doing improvisation, however the key is not to think faster but to actually give up thinking altogether and be in state of relaxed alertness. In martial arts, the Japanese called this state of mind Zanshin (literal translation: remaining mind).
Zanshin is the mental and physical state of all high performance – relaxed alertness – in mindbody. Not relaxed as in sleepy but relaxed in a way that there is no tension in your mindbody. In this state, you are free from thought and simply being aware means you can respond instinctually rather than cognitively.
Stop thinking, be aware. Don’t improvise from cognition. Improvise from awareness. It actually takes less effort and is faster. Simply be present to what is happening inside you, between you and your fellow improvisers, between you and your audience and go with the flow.