This past weekend a friend of mine posted a frantic status on Facebook that his phone would not power on no matter what he did. We typically have a few people come to the service desk here in South Burlington every week with a similar problem. Nearly all of these phones are brought back to life by a very simple two button reboot process.
Hold the power button (the one at the top) and the home button (the one on the face of the phone) both down until you see the Apple logo on the screen. Depending on the status of your battery, you may need to plug the phone in for this to work. In cases where the phone either has a fully drained battery or has crashed this should get it rebooted.