To create a blog website using Strapi as the backend, Nuxt for the frontend, and Apollo for requesting the Strapi API with GraphQL, follow these steps. First, create a new Strapi project using `npx create-strapi-app` and install necessary plugins like GraphQL. Then, create a new Nuxt application using `yarn create nuxt-app`. Install UIkit and Apollo Client in the frontend to style and fetch data from the backend. Configure Apollo Client with GraphQL queries for fetching articles, categories, and other data. Create components for displaying articles, categories, and other pages. Write GraphQL queries for fetching specific data and use markdownit to display content. Finally, navigate through categories using the new components and enjoy your newly created blog website!