You can jam with other people or compose on your own in an improvisational way.
In the former case, you either have to agree on a chord pattern to use (say the simple classic C-Am-F-G in key of C, or maybe G-Am7-D C-D-G in key of G, or even stay on one chord like Am), or you have to be able to recognize chord changes (like the ones in my example). Of course this takes some practice, and DO NOT BE AFRAID TO MAKE MISTAKES. Some people argue that there are no wrong notes ;) Hopefully your ear is good enough to notice when a note you play on the piano "fits" into the harmony of your fellow jammer(s), but you said you are ok with pitch.
In the composing-on-your own case, you have more freedom to experiment (we sometimes call it noodling, and it can bother some players who are more structured, but on your own it's fine). Start with a simple triad in your left hand (say Am, a-c-e) and just play some notes in the RH - any notes at all, even black keys - and listen to how it sounds. String a few notes together. Try some rhythm variations (oom-pa-pa, diddley-dee, diddley-dum, whatever). Find a little motif (against Am you might play e c-d-e c d b-c-d b c for example). Now play a different related triad in LH (say Dm, a-d-f) and find a related motif that "answers" the first one. Play some scale runs, both in the chord (for Am, abcdefga, or even a different scale like e f# gabcde). How does it sound? Like it? Try another key.
Or just take a fragment of a piece you know and modify it a little, either the notes or the rhythm. This can get to be addictive.
One last tip (there are so many): play along to a CD or radio, pop songs maybe.
Good luck, have fun. Remember it's not a job.