First, please ensure that your device is compatible with the app. For example, Disney Karaoke: Frozen is not supported on 1st-generation iPads.
Also, iTunes limits the size of apps that can be downloaded with just a data connection. Disney Karaoke: Frozen is over 100MB, so please ensure that you are connected to WiFi before you attempt to download the app.
After launching the app for the first time, the songs should automatically start to download, as long as you are connected to WiFi. This may take some time, depending on the speed of your internet connection. Do not exit out of the app until all of the songs have finished downloading.