Hp6310 won't print wirelessly with apple airport

I am not familiar with apple - However
Apple suggests resetting the printer system in the link below
https://support.apple.com/en-us/HT203159
Also driver may need updating which can be downloaded from brothers web site.
Other possibility I thought of is the port being used may not match the port that printing uses. port 515 TCP could be being blocked by a firewall of some kind or is not set up correctly.
https://support.apple.com/en-au/HT202944

depends on the printer model....
if you have a recent type of printer with Airprint capability it is very easy to setup wireless.
however if you have an old printer with only a USB-cable you'll need another device to get it working:
Apple sells WiFi-devices like Airport-Express, Time-Capsule and Airport-extreme
Print command central.
The included USB port is great for sharing a printer throughout your wireless network. Time Capsule and the Bonjour networking technology let everyone in the house or office - Mac and PC users alike - take advantage of one centrally located printer.

as this printer has no WiFi function it cannot print directly to an iPad.
however if you have an airport-express router you can connect the printer there with a USB-cable and use it wirelessly...

Canon Support Drivers PIXMA MP250 AirPort Express 802 11n 2nd Generation Guide to ports and connectors

you need to call apple airport technical support number and take the suggestion from their for this
the number is+1(800)-726-0294

APPLE AIRPORT SUPPORT NUMBER 1 800 726 0294 APPLE AIRPORT TECHNICAL PHONE...

it is yor airport. that doen nork correctly

Here's a link to a list of supported printers for the Airport/Time Machine - note that not all HP printers will work - this may be your problem
http://www.ifelix.co.uk/tech/1013.html

did you try going to printer properties? i think you will most likly find your answer there.

Here's what worked for me: I had everything set with my wireless network which included an Airport Extreme base station and two Airport Express units to extend range. I still couldn't plug and play with my printer. 1. You have to plug your printer into the Airport Express, turn it on, then select a document to print from your computer. 2. Select print from the pulldown menu (or select 'command P' on the keyboard). 3. When the print dialog window appears, go to the "Printer:" selection bar near the top of the window and select "print & fax preferences..." 4. This opens a new window, "print & fax." Near the bottom left of this window just below an icon list of your printers are a "+" button and a "-" button right next to each other. 5. Click "+". Yet another window opens which will reveal a list with your printer on it. 6. If you don't see your printer, click the "default" icon in the top left hand corner of the new window. 7. Select your printer, then click "add" on the bottom right hand corner of the window. The window will close automatically and return you to the "print & fax" window. 8. You should now see your printer in the list. You may say, "My printer was already in the list," but that's not good enough. The process you just went through enabled the computer to detect it on your network. You may want to use the "-" button to remove any previously listed printers from the list in the "print & fax" window. 9. Now you should be able to close the "print & fax" window and get some wireless printing done.

mac or windows? Here's the airport express firmware update which resolves a lot of known issue regarding the express.

windows:
http://www.apple.com/support/downloads/airportexpressfirmwareupdate63forwindows.html

mac:
http://www.apple.com/support/downloads/airportexpressfirmwareupdate63formacosx.html

I had the same problem until recently. You have to install the drivers FROM THE CD that came with the printer, instead of selecting the drivers from the default list. Then, when selecting which printer driver to use (you'll have two options) choose Canon IJ and NOT Canon MX310 series. This is a problem with their MX310 driver, which is solved using a default/generic Canon InkJet (hence, the IJ) driver. Hope this helps!
P.S. This only works on Mac OS X. I have yet to figure out how to print wirelessly through Vista. Will keep you posted.