Grand Prize: 100,000 MS points, Xbox 360 Elite
For each Prize Period, you must register by downloading and playing the designated Xbox LIVE Arcade game (full game or free demo).
1. Sign in to Xbox LIVE and access the Xbox LIVE Marketplace
2. Select Game Store
3. Select Xbox LIVE Arcade
4. Select the designated Xbox LIVE Arcade game and Confirm Download
So basically just download the trial games for the specific titles listed on the website between those dates.