You can automate common workflows in New Relic using its APIs to increase efficiency and reduce manual effort. This can be achieved by labeling applications based on their names, setting Apdex thresholds for response time percentiles, and automating these tasks using Node.js scripts that interact with the New Relic API. The APIs allow developers to easily integrate automation into their workflows, making it easier to manage and analyze large numbers of services or application instances. By leveraging API automation, users can streamline processes, reduce laborious manual work, and get more done with less effort.