How can I use 'watch' in my npm scripts?

You can watch your directories using nodemon.

One solution for you is to create three watch scripts, one for each task:

• watch:node-sass,
• watch:html-minifier, and
• watch:imagemin.

Then have a central script watch starting the three:

{
  "name": "personal_site",
  "version": "1.0.0",
  "description": "My personal website.",
  "main": "index.js",
  "scripts": {
    "test": "echo \"Error: no test specified\" && exit 1",
    "node-sass": "node-sass --output-style compressed --include-path node_modules/bourbon/app/assets/stylesheets/ --include-path node_modules/bourbon-neat/app/assets/stylesheets/ 'src/scss/styles.scss' 'dist/css/bundle.min.css'",
    "html-minifier": "html-minifier --collapse-whitespace --remove-comments --remove-attribute-quotes -o 'dist/index.html' 'src/index.html'",
    "imagemin": "imagemin src/images dist/images",
    "serve": "http-server ./dist",
    "watch:node-sass": "nodemon -e scss -x \"npm run node-sass\"",
    "watch:html-minifier": "nodemon -e html -x \"npm run html-minifier\"",
    "watch:imagemin": "nodemon --watch src/images -x \"npm run imagemin\"",
    "watch": "npm run watch:node-sass & npm run watch:html-minifier & npm run watch:imagemin"
  },
  "author": "Dean Gibson",
  "license": "ISC",
  "dependencies": {
    "bourbon": "^4.2.6",
    "bourbon-neat": "^1.7.4",
    "normalize-scss": "^4.0.3"
  },
  "devDependencies": {
    "html-minifier": "^1.3.0",
    "http-server": "^0.9.0",
    "node-sass": "^3.4.2"
  }
}

Read also: How to Use npm as a Build Tool.

I advise onchange, see this boilerplate.

For example,

"watch:css": "onchange 'src/scss/*.scss' -- npm run build:css",

or

"watch:js": "onchange 'src/js/*.js' -- npm run build:js",

No Grunt or Gulp needed!