To set up a private npm registry on Cloudsmith, start by creating a new repository in the Cloudsmith UI or through the API. Next, configure the registry settings to determine what packages will be published and how they are stored. Once configured, you can publish your own packages to the registry, which can then be accessed by developers using npm commands. Additionally, Cloudsmith provides features such as role-based access control and package signing to enhance security. By following the official guide and leveraging these features, developers can easily establish a secure and private npm registry for their organization.