From the words of an HP engineer:
1) Make sure you have Internet connectivity to your printer. Open up one of the Apps on your printer an make sure the content loads.
2) Make sure you have the latest Firmware in your printer. While the C310 does support AirPrint out of the box, there have been Firmware updates since it shipped to make sure everything works correctly. After doing step 1, go to:
Tools->Web->Automatic Updates->Check for Product Updates. This should indicate your firmware is up-to-date or update firmware.
3) Sometimes simply restarting everything (Router, Printer, iOS devices) will clear up any problems you have.