First up, you've got to download the Xbox SmartGlass app. If you already have the My Xbox Live app installed, simply tap on the App Store icon on your device, navigate over to 'Updates', and install the update to Microsoft's old app.
If you don't have the My Xbox Live app installed on your device, you can get the new Xbox SmartGlass app from the App Store here. It's free, compatible with pretty much every iOS device on iOS 5 or higher, and Universal.
On your Xbox 360, make sure your console is updated to the latest firmware and logged on to Xbox Live.
SmartGlass functionality should be on by default, but if you disabled it at some point in the past, you can just go to 'Settings', 'System', 'Console Settings', 'Remote Devices'. On this page, make sure the 'Xbox SmartGlass Apps' option is set to 'on'.
Open up the app on your iOS device, and sign in to the SmartGlass app with the same Xbox Live account as the one currently on your Xbox 360. You can watch the Getting Started videos, or just hit 'Start' to get straight in.
If you aren't automatically connected, hit the button that says 'Connect to your Xbox 360'. Boom, you're in.
'What can I actually do with SmartGlass?' I hear you ask.
Well, you can navigate through your games library and pick the titles you want to play. And if you hit 'Remote', you can navigate the tiled interface of your Xbox 360 with taps and swipes. You can also use Internet Explorer, or search for content with Bing.
You'll also get guides when watching video or listening to music, and you can get some extra info about, and control over, games like Dance Central 3, Forza Horizon, and Home Run Stars.
More SmartGlass-enabled content is coming, Microsoft says.