1. Connect an HDMI cable from PC to HDTV (use dedicated video card output if you have one)
2. Make sure video drivers are up to date.
3. Setup the HDTV in the Video Control Panel (Intel, AMD or NVidia) of your PC. (HDTV section-> 1080pNTSC_60Hz; then adjust OVERSCAN)
4. If you want BOTH screens to display the same content you can CLONE the screens but that can be problematic if they are a different resolution or ratio. You can have the HDTV as an EXTENDED monitor, then you can drag whatever program you want over to the screen.
Other:
I'm not quite sure HOW you're watching hockey on your PC. Your SMART TV should already be connected so maybe there's an app that can do this for you similar to how Netflix works. Not sure why it's on the Internet but not Cable or Satellite.