iPad 2, AirPrint, and HP Deskjet 3520

My grandmother is 90 and recently bought an iPad 2, having previously had little experience with computers. The iPad is her only device i.e. she doesn't have a laptop or desktop. We have just bought her an HP Deskjet 3520 (I think it's this: http://m.hp.com/uk/en/products/printers/product-detail.do?oid=5241239) and my parents have spent the afternoon trying to set it up. Three hours later and no joy. They have plugged in the printer, switched on, the iPad can see that there is a new wireless device (in addition to the broadband router) but does not seem to recognise it as a printer. My parents did not take a laptop with them so are not sure if the initial set up out of the box needs a computer before the iPad can connect to the printer. We were assured in the shop that it would work straightaway and that it was iPad compatible!

Of course it may be very simple but I have never set up a wireless printer before and my parents have never used a Mac or iPad/Phone etc.

My questions are:

1. Does the initial set up need a computer to be present?

2. Are there any other tips/things we've missed?

I will go over tomorrow to try to resolve things and will take any suggestions that you make with me! Thank you.

The iPad is running the latest version of iOS.