To monitor Varnish effectively, you need a dedicated system to store and visualize metrics, alert on anomalies, and correlate with your infrastructure. Datadog can help by collecting and reporting metrics from your hosts, allowing for visualization and correlation on the platform. To start, integrate Datadog with Varnish by verifying its functionality, installing and configuring the Datadog Agent, creating a Varnish configuration file, restarting the Agent, and turning on the integration. Once integrated, you can create custom dashboards to monitor your entire web stack and set up alerts for key metrics like dropped client connections.