Microsoft has revealed a nearly cringe-worthy staged promotional video for the upcoming backwards compatibility feature. While it's very, very staged, it let's us in on quite a bit of information on how the service will work on the Xbox One.
All of your digitally purchased Xbox 360 games will automatically become available on your Xbox One when backwards compatibility goes live, including all of your saves – as long as you saved your game to the cloud and are using the same gamertag on the Xbox One that you had tied to the game.
For physical games, you'll need to put the Xbox 360 game disk into your Xbox One, from there the backward compatible version will be automatically downloaded to your Xbox One. After that, you will still need to insert the game disk into the Xbox 360 to work, but all of your saves, DLC and Achievements will be available on the Xbox One (again via the cloud service).
Oh and there's something cool about feature, holding down the view and the menu button at the same time brings up the classic Xbox 360 Guide.