Suddenly my iPad screen is rainbow colours and not visible. How do I fix??

Try resetting:
Hold the home and power buttons at the same time until the Apple boot logo appears. No data will be lost.

If that fails, try letting the battery drain until the screen shuts off, then after a few minutes charge it back up.

If that does not cure it, then there is likely a hardware issue with your screen and you should indeed take it to an Apple Store.