I'm not sure what they are trying to show.... In the picture it looks like there is some sort of adapter board.
I dunno.... You may have to solder a couple of wires to the barrel connector. There are only 2 wires coming from the power supply (+ and -, or +voltage & ground). You only need to use 2 of the 3 terminals, but you need a way to figure-out which terminals to use and which way to connect them.
If you don't have a multimeter, you can make a power & polarity tester from an LED and series resistor. Test your "tester" on the Arduino to find out which are the +side and -side of your resistor/LED. It doesn't matter if the resistor is on the +side or the -side, as long as they are in series and as long as you figure-out which way makes the LED light-up.