"Free improvisation" is kind of a misnomer. A lot of improvisation is done within very strict structures - limitations, to use phrasing I used elsewhere. For example, most traditional jazz music is in 4/4 time, with circle of fifths western harmony. You can noodle over ii-V-I changes with a swing beat until the cows come home. Because you're settled in this warm bed of familiar grooves, chords, and tunes, everyone has a common language. Any random group of jazz musicians can get together, open up the Real Book, and perform group improvisation. And the audience, also accustomed to the conventions of jazz, can make value judgments and enjoy the performance, unencumbered by needing to figure out a 17/8 ostinato or the sound of just intonation.

I played for years in a free improvisation duo. One of the constraints we used (only for gigs) was "set lists". We would write titles for "songs", and interpret the titles. This helped us have beginnings and ends and moods.

If you're interested in this stuff for serious, seek out the book "Improvisation", by Derek Bailey. He was a famed improviser himself, and wrote a moderately academic book on musical improvisation in a wide variety of different contexts around the world.