First, it must have wi-fi, as it sent a request to print to my desktop computer.

Second, there are a lot of schemes for printing from the Chromebook. Newer printers are equipped to do so directly. There are printers specifically created for Chromebooks. And "Classic" printers require a bit more effort.

One can load an ap into the desktop. When using the Chromebook, hitting 'print' sends the document to the desktop and it can be printed from there. I tried that twice, successfully sent the request over to the desktop (thus indicating there is wi-fi) but it was marked with an "Error". I'm sure with a little more jiggering it can be made to work.

That's what I know so far.