You can use all the physical features on your device (volume control, on/off button, etc.)
Tap on the dot that appears on your screen. On the popup, tap "Device". Press and hold "Lock Screen", then slide to power off.
Depending on what is causing your device's power button not to work, you may or may not be able to turn it on now in the traditional way by pressing and holding the power button. If that fails, connect your device using its USB cord either to a computer or to a wall socket, and it should turn on after several seconds.
Once the iPad turns on you can enable AssistiveTouch by going to Settings > General > Accessibility > AssistiveTouch (under "Interaction"), and swipe the switch to turn on AssistiveTouch.
AssistiveTouch is an accessibility feature designed for people with limited movement capacities. For more information about AssistiveTouch, see this Apple support article.
If AssistiveTouch is not enabled
You will just have to wait for the battery charge to run out.
Not really. There is no other way to control an iPad than by its touch screen. There are limited keyboard controls, but nothing that can replace touch functions.
(If you could get to accessibility settings, you could enable switch control, but you would need to use the touch screen first.)