Current webpack.config.js for using autoprefixer and postcss with webpack 2.1.0-beta.27
const webpack = require('webpack')
const HtmlWebpackPlugin = require('html-webpack-plugin');
const autoprefixer = require('autoprefixer')
module.exports = {
  entry: './index.js',
  devtool: 'inline-source-map',
  output: { filename: 'bundle.js', publicPath: '' },
  module: {
    rules: [
      {
        test: /\.css$/,
        use: [
          'style-loader',
          { loader: 'css-loader', options: { modules: true, importLoaders: 1 } },
          { loader: 'postcss-loader' },
        ]
      },
      {
        test: /\.js$/,
        use: [ { loader: 'babel-loader', options: { presets: ['es2015', 'react', 'stage-2'] } } ],
        exclude: /node_modules/,
      }
    ]
  },
  plugins: [
    new HtmlWebpackPlugin({ title: 'Example', template: './index.html' }),
    new webpack.LoaderOptionsPlugin({ options: { postcss: [ autoprefixer ] } })
  ],
}
Note: The LoaderOptionsPlugin is a 'polyfill' required in webpack =< 2.1.0-beta.24. I will update this answer when I work out the new syntax.
Running it:
Have the following relevant packages in package.json:
"dependencies": {
  "autoprefixer": "^6.5.4",
  "babel-core": "^6.7.6",
  "babel-loader": "^6.2.4",
  "babel-preset-es2015": "^6.6.0",
  "babel-preset-react": "^6.5.0",
  "babel-preset-stage-2": "^6.5.0",
  "babel-register": "^6.7.2",
  "babel-runtime": "^6.6.1",
  "css-loader": "^0.26.1",
  "postcss-loader": "^1.2.1",
  "style-loader": "^0.13.1",
  "webpack": "2.1.0-beta.27",
  "webpack-dev-server": "2.1.0-beta.12"
}
And the following relevant script in package.json:
"scripts": {
  "dev": "NODE_ENV=dev webpack-dev-server --port 3000 --inline --hot"
},
And run it with 
yarn install
npm run dev