Hi KazuMae!
Unfortunately the way to install an APK from outside of Google Play is a little annoying, but I'll put the steps below:
1) Before you can install apps to your phone from the web, you need to make sure that they're allowed on your device. Go to Menu > Settings > Security > and check Unknown Sources to allow your phone to install apps from other sources.
2) Download the APK to your phone. Navigate to the file and click on it to begin installation.
3) Once it's installed, you'll be able to play the game!
We're currently in the process of getting the demo onto Google Play, so if you can't work it out then you'll be able to download it from there easily soon.
Thank you for your support of TDS!