This is a sample Gruntfile to run the basic 'jekyll build' with local server and livereload on changes. The grunt plugin can do this stuff without connect/watch, but I wanted more control over the options for other build steps.

grunt jekyll basic

module.exports = function(grunt) {

  grunt.initConfig({
    pkg: grunt.file.readJSON('package.json'),

    watch: {
      default: {
        files: ['**/*.*', '!_site/**.*'],
        tasks: ['jekyll'],
        options: {
          livereload: true
        }
      }
    },

    connect: {
      default: {
        options: {
          hostname: 'localhost',
          port: 9000,
          livereload: true,
          base: './_site',
          open: { appName: 'chrome' }
        }
      }
    },

    jekyll: {
      default: {

      }
    }

  });

  grunt.loadNpmTasks('grunt-contrib-watch');
  grunt.loadNpmTasks('grunt-contrib-connect');
  grunt.loadNpmTasks('grunt-jekyll');

  grunt.registerTask('build', ['jekyll']);
  grunt.registerTask('default', ['jekyll', 'connect', 'watch']);

};