Instructions
Go to the Xbox main menu. This will come up if the console is turned on without a game inserted. It can also be reached by using the "Xbox" button on the controller.
Choose the "Xbox Live Arcade" option in the menu.
Choose a game type from the arcade menu.
Select the game you wish to download.
Select if you want to download the full game or a demo version of the game.
Confirm that you wish to purchase the game if you are downloading the full version. There is no prompt if you are downloading the free demo version of the game.
Choose the "Download Now" option from the menu to start downloading it to your hard drive.