Currently, installing tailwind (without specific versions) will not easily work with Gridsome, because of incompatibilities with Postcss 8.

You may get errors when running gridsome develop such as true is not a PostCSS plugin. This is likely due to PostCSS 8.

Here is how I got around these issues...

Add these dev dependencies to package.json:

    "@tailwindcss/postcss7-compat": "^2.0.2",
    "autoprefixer": "^9",
    "gridsome-plugin-tailwindcss": "^4.1.1",
    "postcss": "^7",
    "tailwindcss": "npm:@tailwindcss/postcss7-compat"

(and run yarn to install them)

Then in gridsome.config.js:

// import tailwind at the top of the file
const tailwindcss = require("tailwindcss");

module.exports = {
 // ... (the rest of your config)

  css: {
    loaderOptions: {
      postcss: {
        plugins: [
          tailwindcss
        ],
      },
    },
  },

  plugins: [
    {
      use: "gridsome-plugin-tailwindcss",

      // these options are optional, as they are copies of the default values...
      options: {
        tailwindConfig: './tailwind.config.js',
        presetEnvConfig: {},
        shouldImport: false,
        shouldTimeTravel: false
      }
    },
    // ... the rest of your plugins
    ],
}

And lastly create a tailwind.config.js:

module.exports = {
  purge: [
    './src/**/*.vue',
    './src/**/*.js',
    './src/**/*.md',
    './src/**/*.html',
  ],
  theme: {
    // your tailwind config goes here
    // container: {
    //  center: true,
    // },
  },
}

And it should work! You can try it out by adding this in a vue component:

<p class="text-2xl mb-2 text-black text-center">Example of tailwind</p>

Or in your index.js add

require('./app.css');

And in app.css add some tailwind such as:

@tailwind base;
@tailwind tailwind;
@tailwind components;

body { background : bg-red text-blue; }

Probably by the time you read this the issues are resolved. The exact version of Gridsome that I used this with was 0.7.23.

(The config above will auto prune unused Tailwind css rules, to keep your css file size down.)