You can download a selection of free apps and games at Zune Marketplace to use and play on your Zune HD. Just make sure you're using the latest version of the Zune software.
Note Before attempting to download apps, first make sure that your Zune is linked to your Zune Tag, otherwise the download will fail. You can do this in the Zune software by going to Settings, Device, Linking.
Download games and apps to your Zune HD
Connect your Zune HD to your computer and sign into the Zune software.
Click on Marketplace, Apps.
Select the game or app you want, then click Download.
Go to Collection, Apps, and drag the games and apps that you want to the Zune player icon to sync them.
To access games and apps on your Zune HD, on the home screen tap Apps, then tap the game or app you want.