Through the Dashboard
"Risk: Factions" can be purchased through the "Game Marketplace" tab in the Xbox Live dashboard. The game can be found alphabetically under "R," or you can narrow your search by first highlighting "Arcade," then "Card and Board Games." Once you've entered the download screen, press the "X" button to add Microsoft Points if you don't have enough points in your account. Highlight "Confirm Download" and press "A" to complete the purchase.
Through Xbox.com
If you have a Windows Live ID, you can sign in to Xbox.com and purchase "Risk: Factions" through your computer. Type the name of the game in the field at the top of the screen, then "See All" to view the available downloads. Select "Full Game," then "Download to Xbox 360" to complete the process. You can also add Microsoft Points to your account through Xbox.com if you need to.
Game Demo
You can download a free trial of "Risk: Factions" if you'd like to try the game out before buying it. The "Demo" option is available through both the dashboard and Xbox.com.