However, I don't just want to turn a TV on and off, I want more buttons so I can fully control a TV. How can I wire 4 more buttons, to make this more capable?
There is no schematic in the link you provided, just a useless Fritzing picture that is wrong anyway.
But, the Uno has at least four more GPIO pins where you can add more buttons.
Buy a few buttons, LEDs and 1K resistors. Experiment with the basic example sketches on the IDE.