Hey @(you need an account to see links), great question. To unplug your internet modem, simply remove the power cord from the modem. Do the same for your router if it is a separate unit. This will effectively turn off your modem. Unplugging the cord from the outlet will accomplish the same.
1. You don't have to shut down anything besides your modem/router. I would also type these in command prompt (if Windows user)
Code:
ipconfig /release
ipconfig /renew
2.Yeah unplug them both, doesn't matter what you unplug really. Let them sit unplugged for 1-2 mins. Plug the modem in first and wait 30 seconds then plug in your router.