10 thoughts about improvisation:
1) Do no harm.
2) If you aren't feeling anything to add, either shut up or do something you never could have imagined yourself doing in that situation. Be bold - change the music, or don't.
3) Whatever you do, do it forcefully. Fully commit to every gesture you make.
4) Note about #3 - forcefully does not necessarily mean loudly. If you stop playing altogether that can be the most aggressive act imaginable. It all depends on context and intent.
5) When you are playing, cultivate a total disregard for what others might think of what you are playing. In fact, disregard what you might think about it. Later on, if at all, is the time for such thoughts.
6) Think like a composer: own all the music, not only what you play but what others play. Do not separate what is "yours" based on something so trivial as who is physically playing it. If you are improvising, you are playing all the music.
7) Never ever (almost never ever) imitate - it's the cheapest form of communication. If you must respond, respond on a parallel plane. Remember, "interaction" is overrated.
8) Don't try too hard. Don't try to make things "work." We aren't trying to make chairs. Human beings are complicated, and so is their art. They, and it, often don't "work." Especially don't try and play music. If it sounds like music, it probably isn't.
9) Don't practice something on your own and then insert it into an improvisation - this means you almost certainly have not been listening.
10) Beware of "strategies." Strategies are for golfers and hedge fund managers and are useless if you want to get to something authentic. Because what, in the end, are you trying to do, other than take what is in your insides and compare it with and connect it to all the other insides? Strategies, techniques, etc are all false choices. You might get oohs and ahhs, but you will not have an epiphany. Trust me, the epiphany lasts a lot longer.
and one more, the most important:
11) In the heat of battle, ignore 1-10.