Download Demos and Play Them on Xbox 360

Playing game demos are a great way to 'try before you buy!'

Steps

Check if you're are on Xbox Live. If not then there are no demos available for offline users. (Unless you buy a magazine with a demo disk in it.) If you are online, read on.
Go to 'Xbox 360 Dashboard' then go to the game marketplace.
Go to the demos option on the marketplace, and find the game you want.
Click download (on the game demo) and wait for the download to start.
When the download is complete, press the Xbox button on your controller.
Go to quick launch and press the right button on your d-pad.
Select the demo you want and hit A. Your demo should load. Have fun!