I expect that you are using the browser print function on the laptop. I choose the "Print" option from the box-with-up-arrow icon in the iPhone banner at the top. But I seem to recall that the 'Print' option in that box/arrow icon wasn't available on a site that I visited once. Probably a copyright issue. But if you are getting to the "No AirPrint printers available" error, you have to be doing a lot correctly. ...Stupid question, but you are on your WiFi with your iPhone...yes? ...Settings-WiFi-Select-Password...
I'm using Airprint on an Epson NX430. I can print both eMail and 'Notes' from my iPhone 6 without special configuration. I do get a 'Choose Printer' screen and my NX430 populates on the next screen, which I then have to select. I don't see anywhere in my iPhone 6 to configure a printer, it just happens.
I also print the puzzles from my local paper on a very old iPad using the browser (Safari). The printer access there is within the newspaper app. I can print from my browser too, but it formats badly.
Good luck.