As you might expect, Chrome plays nicely with Google Cloud Printing (the default printing method for ChromeBook's). Cloud printing allows users to print to any connected printer from anywhere. It's easy to set up any Cloud Ready printer, just follow your manufacturer's provided instructions. But if you have a classic printer, you can still hook it up to Cloud Printing, as long as it's connected to a computer on which Chrome is installed and any remote printers are logged into the same Google account.
To set up your printer on the associated computer's Chrome browser, goto 'Settings->Printing->Google Cloud Print' and click on 'Manage Cloud Print devices' to add or remove any printers. Here, you will also find the ability to add an option to save any documents as PDFs on your Google Drive account.