Hold down the power button and the home button at the same time until you see the Apple logo. May take up to 10 secs or so. Release the buttons once you see the logo. It's like a computer so give the phone time to reboot.
Just FYI, if that seems to do nothing, plug it into the desktop machine running itunes. It may have drained itself completely and might revive with a little juice. It could take a few minutes to charge up... so charging it for an hour or so and then hitting the two button reboot can bring it back.
If all else fails, visit an apple store... they can revive it unless it's completely dead.