To start a development server and enable the live preview in Storyblok all you have to do is to start your local dev environment:
npm run dev
Storyblok will embed your dev/test environment in their SaaS and enable you to create new content entries on the fly. During the getting started you did execute the content seed which already set the preview URL to the default
http://localhost:3000/. You can always change this in your Storyblok space settings to, for example, host a development stage to have an instant preview for your editors as well.