Ansible is used to automate the installation of the Datadog Agent on a dynamic inventory of Windows hosts. The process involves building an Ansible inventory, connecting the control node to managed hosts via WinRM, and installing the Datadog role with necessary modules to download and install the Datadog Agent. Once installed, users can configure various integrations such as SQL Server and Live Process monitoring, enabling deeper insights into their environment. The process also includes encrypting sensitive data like API keys using Ansible Vault or secrets management packages.