The outlet in the other room might already be active, so try it first by moving the cable box from one room to the other.
There will be at least one splitter in the house, and possibly more. It might be in the basement, garage, crawl space or outside near the electric meter If the TV outlet in the new room is not connected, then look for the splitter and look for any disconnected coax. You might need to disconnect a existing TV line that is not being used so you can connect the coax for the new room.
As each house is wired differently, there is no one answer that fits all situations. You might find a friend that's handy, or end up hiring a low voltage specialist or Comcast if you can't get the TV outlet active.