Assuming it has worked previously, do a Reboot: Press and hold both the home and power buttons at the same time for at least 10 seconds (hold past the swipe to shut down if it appears) until the Apple Logo appears, and your iPad should come back to life.......
It may be that your iPad is out of battery. In that case, simply plug in the charger like you are recharging it, then wait. After a period of time (around 10 mins.), it should start again.
You might have to Reboot too. In that case, as rbrylawski said, press the Sleep button and the Home button together for at least 10 seconds. See if it starts up.
If none of these work, try going to an Apple Store for help. It may be that your battery is not rechargeable anymore and needs to be replaced.