(Disclaimer: I’m not an expert on improv, and this information is all based on my own experience unless noted otherwise. All the movement improv I’ve done has been supervised by a teacher, and in a dance studio, so I can’t necessarily advise on doing it in other settings.)
There are many kinds of improv--maybe you’ve heard of contact improv, improv comedy, or some other kind. I’ve done a fair bit of improv in dance classes, particularly in the past year, and what I’ve found is as I’ve done more, I’ve gotten more comfortable making quick decisions, even when not dancing. I have a tendency to second-guess myself, and improv helps me get used to resisting that. My brother, who does comedy improv, has also found improv helps with quick thinking.
In my experience as a dancer, the improv I’ve done has generally been structured improv: improvisation with certain limitations imposed, rather than totally freeform movement. One exercise I did this summer that’s fairly simple to do alone is to imagine a ball moving around inside your body. You move your body as the “ball” “moves” through it. You might change the weight of the ball, the (imagined) substance the ball is moving through, or the number of balls.
Outside of improv I’ve done at dance, something else I’ve done that helps with quick thinking is playing a card game called Anomia. The deck has cards with several different symbols, each with a word or phrase, such as “address” or “cause of death.” Players take turns drawing cards, and if two players have cards with matching symbols, they say something that fits the word on the other player’s card. Whoever says something that fits first gets that card, and it can go very fast.
Have any of you done improv? Feel free to talk about it in the comments!