My older HP Envy printer had instructions onscreen for setting up an ad hoc network. You need to set up the printer wifi network from the printer then join that network from a phone or iPad.Could you post the model number of your printer?
And if your printer does have wifi network capability, then what you do is find the printer from your iOS device. You go to Settings > wifi, and turn wifi on, and see if your printer shows up as a wifi network.
I did also play with setting up a printer network with the Airport Express, just because I was interested in the possibility of doing it. IIRC, there were various error lights that blinked (because there is no internet access) but the process was simple.