Cessna pilot reported they were focused on coupling the auto pilot to the GPS on approach and descended below Final Approach Fix crossing altitude.

Narrative

I was doing some approaches in my new to me Cessna 206. I was not current and was still not comfortable with the avionics. I was flying with a CFII with the intention of trying to couple the autopilot to the GPS glide slope output on the LPV approach. I was given vectors and told to intercept the final approach coarse; which I did. The FAF has a minimum altitude of 1;500 ft. I had not successfully coupled the autopilot to the GPS approach so I was trying to following the glide slope using the VS mode and also troubleshoot. I allowed the aircraft to descend too low. I was at 1;100 ft. when I noticed my error. When I realized I was too low I looked up and noticed I was below the overcast; and had the airport in sight. I disconnected the autopilot and proceeded to a full stop landing. Later I discussed why had happened with the CFII. We determined that we both got too focused on the avionics and not on the approach. That evening I read more about the avionics and proceeded to fly again the next day doing one practice approaches in VMC and was successful with coupling the avionics and autopilot. A few days later I contacted TRACON about the situation. We had a good chat about Minimum Vectoring Altitudes and why the altitudes are established the way they are.