To troubleshoot iPhone 5c problems you first need to identify the specific issue. Typical iPhone 5c problems include being unable to delete both stock and downloaded apps, issues with the white or black screen, and the display being stuck in grayscale.
An iPhone's settings may be stopping you from deleting apps. To fix this, go to Settings, then General, Restrictions, and Deleting Apps. Make sure that the feature is turned on.
If the display turns from white to black and is non-responsive, restore your phone in DFU mode. First, backup your phone's data, hold the power button for 3 seconds, then press the home button while still holding the power button. Release the home button while still holding the power button for 10 seconds, and now your device should prompt with the "Connect to iTunes Screen."
Connect your phone to your computer, click your iPhones image on iTunes, select the Summary tab and click Restore. If successful, the device restarts. Follow the steps given by the iOS Setup Assistant.
If your phone is still in grayscale and the grayscale button is turned off, then reboot your phone. Otherwise, you must reset it. Press and hold the Sleep or Wake and Home buttons for 10 seconds, until you see the Apple logo, which causes it to reset.