Here are some resources that will help you start taking advantage of ES6 today.
The sixth ECMAScript specification was finalised in June 2015, and there is now a flurry of JavaScript features coming our way. These resources will help you decide whether you want to make the jump to ES6, and if so, provide the guidance you need to start using the new features.
I wrote a series of over 20 articles that will give you a comprehensive understanding of ES6. Each article covers a specific feature or aspect of the language that is specific to ES6, and they're easy to navigate with tons of examples and practical considerations.
These articles cover all the basics, in addition to promises, rest and spread, iterators, generators, proxies, collections, changes to Math, Number, Object and String, classes, symbols and reflection. It's a great way to dive head-first into ES6.
While he doesn't have a formal series on ES6, Axel Rauschmayer has written dozens of detailed articles describing the technical depths of ES6. He's also putting together a book, Exploring ES6.
When you get started with ES6, you'll quickly realise no browser currently supports ES6 100 per cent. In the meantime, you can leverage these compatibility tables to understand what features are implemented across what browsers. Alas, these tables are mostly useful for research, as your best bet when it comes to using ES6 today is to rely on a transpiler like Babel.
If you want to get started right away, your best bet might be to hop into the Babel REPL and start toying around with it. There's a great article for learning the basics of ES6 language features and syntax.