The setup involves installing the Prometheus Operator, which manages Prometheus and Alertmanager with custom resources in a Kubernetes cluster, and then configuring it to scrape metrics from a YugabyteDB pod using the ServiceMonitor Custom Resource. The Helm chart also provisions Grafana for visualization of the collected metrics. After setting up the monitoring system, a client workload is run on the YugabyteDB cluster to generate more metrics, which can be visualized in the Grafana dashboard.