Here are a few things you can try to make it work:
Make sure your device is up to date. The latest software is 8.1.
Finger and Home button should be clean and dry.
When you use Touch ID, cover the Home button completely, don't press down hard or too quickly, your finger should touch the metal ring around the button. A case or screen protector shouldn't cover the button or the ring around it. If it does, remove it.
In Settings - Touch ID & Passcode, iPad unlock or iTunes & App Store has to be enabled.
Add a different finger as Touch ID.
Something that helped other users: addthe same finger for a second or third time.
If all this doesn't help, take your iPad to an Apple Retail Store.