The deploy-mdbook action allows you to easily build and deploy your mdBook project to GitHub Pages. See action.yml for configuration options.

name: Deploy mdBook
on: [push]
jobs:
  build:
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v2
      - uses: XAMPPRocky/deploy-mdbook@v1.1
        with:
            token: ${{ secrets.GITHUB_TOKEN }}

The action is written in NodeJS 12, and you can install the dependencies with:

npm install

npm start

GitHub Actions requires all the dependencies to be committed, so before creating a commit you need to run:

npm run build

The command will bundle everything in dist/index.js. That file will need to be committed.