By default, you can use shift+prtscr to capture a portion of the screen.
Then if you have Screenshot Captor set up with default settings you'll see a pop-up dialog where you can choose print.
Or you can change SC options to autoprint after every capture and stay minimized.
You can also see options for adding captions to your print jobs, and doing more stuff -- but try first thing first and let us know if you have any trouble.