What model HP printer is it?
Go to Settings / WiFi is it on and connected to the same network as the printer?
If so then just go to Print from any AirPrint enabled app and you should see the printer listed:
Is that the exact model number or is it HP Photosmart D110a?
I am not seeing that that model has AiPrint only the D110a has that?
Do you have a Mac computer?
I think there might be a firmware update that will allow Airprint. Go to the menu and look for updated firmware:
OK no problem
Do you have a Mac or Windows computer?
If you do not see the printer after installing the firmware update and restarting the printer, then going to PRINT from any Apple app like Mail... then the printer is not capable of that. If you have a Mac computer you can install Handyprint and then your iPad can print to ANY printer your Mac can print to:
Let me know when you have time to do this.