When improvising music, especially when
improvising with one or more other musicians, one must choose the musical
language (or the lack thereof, which is a
meta-language itself). This can mean an agreement upon a certain
jazz style, or
tonality, or
atonality, or a
completely open spectrum between many styles of music.
Once the context is established, all one needs to do is listen and react. In solo improvisation, "listening" can mean anything from attention to the ambient sounds in the room to an attention to the music within oneself. Through the practice of deep listening, these two sound worlds may merge. This is a Good Thing. In group improvisation, one may listen to the sounds made intentionally by the other musician(s), or to the impact of their physical presence in the space.
One may react to these sounds in silence, letting the pre-existing sounds speak for themselves. One may react against the sounds, in an attempt to change the sound world. One may also accompany the sounds, paying attention to complement and supplement the whole sound environment.
In improvisation, above all else, one must be fully engaged in the act of music, and try to avoid the pitfalls of insecurity, egomania, and other non-musical distractions.
... and have fun!