Microsoft's update to thebrought along support for controlling an Xbox 360 straight from an iPhone. (The update was rolled out across all iOS platforms, but for whatever reason, this feature only works with an iPhone.) Here's how to get it to work.
First, you'll want to make sure that your Xbox 360 and iPhone are connected to the same Wi-Fi network. You can check the Wi-Fi status by going to settings on the iPhone and network settings on the Xbox. Once you've confirmed that both devices are using the same Wi-Fi, head over to the settings area again on the Xbox and then enter Console Settings. From there, you'll want to navigate down to Xbox Companion. Click on Available, then return to the home screen. Your Xbox is now ready to interact with any kind of companion application.
If you haven't already done so, download the My Xbox Live app from the App Store, run it, and log in with your Xbox Live credentials. One connected, you can initiate a companion link-up by sliding over to the Quick Play menu. A green title in the middle should say "Connect to Xbox." Click on the button and a notification on the screen of your TV should flash indicating that you've made the connection. Now take a look at your iPhone's screen. If a layout of Xbox buttons hasn't automatically shown up, click the three dots in the corner to bring up the menu, and select Controller.
You should now be able to navigate through the Xbox menu using the onscreen buttons on your iPhone. Functionality really doesn't go beyond that, but it might be easier to scroll through the Xbox's various media apps and content delivery portals this way.