Try the standard troubleshooting steps in this order:
Restart: Press On/Off button until the Slide to Power Off slider appears, select Slide to Power Off and, after It shuts down, press the On/Off button until the Apple logo appears.
Reset: Press the Home and On/Off buttons at the same time and hold them until the Apple logo appears (about 10-15 seconds). No data will be lost.
Restore: Connect your device to iTunes on your computer, backup, and then select Restore to Factory.
See here for more details on restore: https://support.apple.com/en-us/HT201252
If none of these work your device may have developed a hardware problem. Contact Apple Support: http://www.apple.com/contact/