We are third year medical students in a longitudinal integrated clerkship.
We became frustrated by many of the systems issues we witnessed. This prompted us to get together and discuss what we were seeing.
Rather than accept the system as it was, slowly becoming blind to the inefficiencies and breakdowns in the system, we decided to share our experiences. Our meetings were informal gatherings at a student's apartment (with plenty of snacks).
After each participant shared a story, the group would reflect by sharing similar experiences, identifying the specific points at which there was a breakdown, and brainstorming about what could have been done differently.
Each student typed up his or her story along with the major discussion points. These documents were compiled into a "scrapbook" on a password-protected hospital server.

At the end of the year, we met with the hospital's CEO. We shared stories, but mostly introduced him to the medical students as a set of eyes on the ground that he could look to for information about what needed to change in the system.

All it takes to start a Systems Rounds is to gather a group of students interested in keeping their eyes open and discussing what they see. Set a date and have people bring at least one or two stories.