This tutorial is for a 1998 323is. From what I understand most 3 series in the e36 (and even the e46?) are very similar with regard to the ignition switch. Other users have said this worked on their Z3 too.
My key would occasionally spin and be tricky to start. I never worried about it until it came out with my car still running and I couldn't turn it off! This is a video of how I fixed it. After you get it fixed, try to push the key in while turning your car on or off, and this should help prevent it from happening again.