Several iPhone functions and apps can cause the battery to drain quickly: Wi-Fi, Safari, notifications, badges, pushing email, and more. Alternatively, your iPhone may power off as the result of a non-power-related issue, such as a memory shortage or storage device failure. How you power your iPhone back on depends on the reason it died.
Plug an iPhone with a battery that has died into a power source. If you are connecting the iPhone to a computer using the USB cable that came with the device, be sure to connect to a high-power USB port. High-power USB ports can be found on the computer's tower or on a monitor that contains the hardware typically found in a monitor; USB ports found on a keyboard on a standard monitor are low-power ports and will not charge your device. The Apple logo appears on the screen when your iPhone has enough power to use.
Hold down the iPhone's "Sleep/Wake" button if the device died as the result of an issue unrelated to power. The Apple logo will appear on the screen to indicate that the device is successfully powering on. Plug the iPhone into a power source -- even if it didn't die due to a power shortage -- if several hours or days have passed since you last used the device, as your device may have lost battery over time.
Perform a soft reset on your iPhone if it won't power back on otherwise. Hold down the "Home" button at the same time as the "Sleep/Wake" until the Apple logo appears on the screen.
Take your iPhone to an Apple repair representative if you are convinced the device is fully charged but won't turn on. Your iPhone may be experiencing an electrical failure, dead battery or some other issue it isn't possible for you to resolve on your own.
Do not attempt to replace a dead iPhone battery without the aid of an authorized Apple representative. Damage you inflict while doing so isn't covered by your iPhone's warranty and may void the warranty altogether.