iOS devices can only print directly to AirPrint printers.
To print directly from an iPad / iPhone you will need an AirPrint compatible printer or another device to act as a print server. That can be a Mac computer running Printopia ($19.95 with free trial) or handyPrint (donation - supported). The Mac must be "on" but may be asleep for them to work. Equivalent PC options exist but you're on your own finding them.
You can also buy this standalone print server:
The xPrintServer Home Edition will support a directly connected USB printer. The Network Edition will support any network printer.
These options enable you to use any printer available to your Mac, even older ones that may predate AirPrint by decades. Otherwise you will need to buy an AirPrint printer or multifunction device. The following are my recommendations:
Read the reviews and choose wisely.