The current document is directed to an automated-application-installation subsystem that provisions, installs, and configures applications across cloud-computing providers. The automated-application-installation subsystem employs an application blueprint to identify components to provisions, including component specifications and constraints, and to identify interdependencies between components. The automated-application-installation subsystem then determines a cost-effective provisioning of the identified components across available cloud-computing providers and installs the application according to the cost-effective provisioning. When less expensive, storage and computer-instruction-execution components of the application may be allocated from different cloud=computing providers.