Up to now Chromebooks could only print by sending your document up to the cloud and back to the printer.
That process created a huge problem here at Happy Valley where the command to print never reaches the cloud at times. (Your router keeps a record of those interruptions which is accessible to review. I type in http://192.168.100.1/ to do so.)
Anyway. that problem is about to be solved for selected printers. You need to upgrade to Chrome OS 59 for it to work.
The new print process sends your print job locally to your printer via the router and your local area network. Only selected Hewlett-Packard printers could do this in the past, although there are other extensions to accomplish the result.
For this process to work you need to know your printer's IP address.
There are various ways to find it..
The newest printers display the IP address on the control panel, once set up on the same panel. Older printers may require set up on a Windows device.
I use the Android smartphone app called Fing to establish and confirm which printers and IP addresses are available on my network.