To get started with RubyGems and Cloudsmith, you can create a private repository in 60 seconds and then push a RubyGem to it. The process involves creating an entitlement token and using it to authenticate with the Cloudsmith API. Once the Gem is pushed to the private repository, you can pull and install it on your system. Additionally, Cloudsmith supports multi-format repositories, which allows you to manage different formats of your Gems in one place. The official guides provide more detailed information on how to create a repository and use entitlement tokens for authentication.