What is the recommended way to use native javascript libraries in react native? Are there any specific restrictions?
Easy peasy! From the root of your project just run:
npm install moment --save
Then you can import it in your code:
import moment from 'moment';
var now = moment().format();
The restrictions would be anything that tries to "reach out" to the browser (which doesn't exist in this context). That's why there's polyfills for things like XHR.
The official documentation has examples on how to use the moment library