You will need an AirPrint compatible printer to be able print from the iPhone or iPad.
Unfortunately, simply connecting a printer to the USB port on an AirPort Express does not make it AirPrint compatible.
Check this Apple support document to see if your printer might be on the list of compatible models.
If your printer is not on this list, there might be a possible workaround if you install an App like Printopia on your Mac. There is a free trial, so you will know in a few minutes whether this will work for you.