It looks like you're using types from Typescript, while your code is in a plain Javascript file (.js). nav: NavController declares that nav is of type NavController.
When you run ionic serve, Ionic runs webpack to compile and package your code. Since this is not a valid JS syntax, it fails.
Ionic 2 is based on Angular 2, which was written in Typescript. While Angular 2 can be used with plain Javascript, it is mostly undocumented, and they basically recommend using Typescript when developing Angular 2 applications.
When you create a new Ionic 2 project, you should use the --ts flag if you want your project to be in Typescript. The command should be:
ionic start MyIonic2Project --v2 --ts
After that, copy-pasting the Ionic 2 tutorials should work for you.