It happens. iPads freeze up and become completely unresponsive. The screen doesn’t respond; the home button doesn’t work; the sleep button doesn’t work; holding down the sleep button to power down doesn’t work. Now what?
A hard reset.
To perform a hard reset hold down the Sleep and Home buttons simultaneously (like you do for a screenshot, but hold them down) for about 10 seconds. If the swipe to power down option comes up, ignore it and keep holding the two buttons down. After about 10 seconds the iPad will power down and reboot (you’ll see the Apple logo when this happens). This is the equivalent of holding down the power button on a desktop/laptop to force a power down when they freeze.
Needing to perform a hard reset on an iPad (or iPhone) should be a very rare occurrence, but it’s a good trick to know.