The Softlayer API allows users to automate tasks like managing servers and infrastructure. It has over 260 services, 3,183 methods, and 15,816 properties. Common tasks that can be automated include provisioning servers, managing object storage, and implementing messaging queues. The API uses a hierarchical structure of services and supports REST, SOAP, and XML-RPC. Useful resources for learning the Softlayer API include its documentation, code samples, and Python client libraries.