Grafana is a versatile visualization tool that comes with built-in plugins for data sources like Prometheus and PostgreSQL, allowing users with administrative privileges to connect and visualize data from compatible databases. To integrate TimescaleDB with Grafana, users must first install Grafana and create a Timescale service by signing into the Timescale portal, creating the service, and downloading a configuration file containing necessary credentials. Once the TimescaleDB service is set up, users log into Grafana, navigate to the data sources configuration, and add a PostgreSQL data source using the credentials from the downloaded file, ensuring to set the TLS/SSL mode to "require" and enable TimescaleDB. After successful configuration, users can create data panels using SQL and further explore data visualization through tutorials like the NYC Taxi Cab tutorial.