What is the proper way to turn an Arduino UNO into an ISP?
The wiring is actually identical. It just uses the ISP header (2x3 pins) on the target board, instead of the pins 5v, GND, RST, 11, 12, 13. Just like the table you added says.

The downside to using the ISP header, is you need a male to female wire for connecting. Upside is you can easily take of these 6 pins, and connect it to a different arduino to be programmed.

I always needed to add a capacitor between RESET and GND. The exact value isn't that critical.

The reset pin is the one to the left of 3v3.