There are two problems here. First, you need a package.json file. Telling npm to install without one will throw the npm WARN enoent ENOENT: no such file or directory error. In your project directory, run npm init to generate a package.json file for the project.

Second, local binaries probably aren't found because the local ./node_modules/.bin is not in $PATH. There are some solutions in How to use package installed locally in node_modules?, but it might be easier to just wrap your babel-cli commands in npm scripts. This works because npm run adds the output of npm bin (node_modules/.bin) to the PATH provided to scripts.

Here's a stripped-down example package.json which returns the locally installed babel-cli version:

{
  "scripts": {
    "babel-version": "babel --version"
  },
  "devDependencies": {
    "babel-cli": "^6.6.5"
  }
}

Call the script with this command: npm run babel-version.

Putting scripts in package.json is quite useful but often overlooked. Much more in the docs: How npm handles the "scripts" field

The @ signifies the usage of an "npm scope":

https://docs.npmjs.com/about-scopes

It's basically a way to avoid name clashing, so we could both own modules @cdbrouk/foo and @jedrichards/foo. Babel moved to using the @babel scope a while ago, so the @babel/... modules are the correct ones to use.