You can print directly to most printer models over WiFi without extra software.
AirPrint is not required to be able to print. You can print from your iPhone/iPad to ALL printers using the free WePrint printer sharing software which is installed on your Mac or PC from here:
https://esz.nz/wp

If your printer has a USB or other connection type, you can also use WePrint to share the printer with your iPhone/iPad.