You can learn to Tap in about an hour by using the TapGenius Game, available on the iOS App Store. There are 8 'Tap-Sets' which are taught via musical and visual tutorials, and are followed by rounds of gameplay. It takes approximately five hours of practice to become a fast, proficient tapper.
On Android, you can learn to tap with the TapTutor App on the Play Store.
Here is a video overview how to learn with TapGenius: