Deploying the New Relic infrastructure monitoring agent on Amazon EC2 instances can be done quickly and easily. The process involves launching an instance, configuring advanced details to deploy the agent, and waiting for data to start being sent within 60 seconds. To simplify the deployment, users can use AWS CloudFormation or automation tools. A step-by-step guide is provided, including a script that needs to be copied and pasted into the User data field during launch configuration, which installs the agent and enables data ingestion in under a minute. Once deployed, users can start seeing data in their New Relic accounts within 60 seconds, making it an efficient way to monitor infrastructure performance.