To monitor YugabyteDB with Prometheus on Docker, start by installing YugabyteDB and running a sample key-value workload. Then, prepare a Prometheus configuration file to scrape metrics from YugabyteDB's /prometheus-metrics endpoint. Start the Prometheus server and open its UI to analyze key metrics such as read/write throughput and latency for the CassandraKeyValue sample app. The configuration file uses labels to group targets by node type, allowing for detailed monitoring of each layer of YugabyteDB.