4 Digit, 7 Segment Display Wiring (14 pin)
It's just a 12 pin display, but with two extra pins for the colon.

Removing connections can help you better understand what it going on. 

Resistor should be added to the anodes (pins 1,2,3,4,5,8,9,12,13) just like on the website. Pin 8 should be a different value, to match the brightness of the other (multiplexed) leds.

The other end of the resistor can be put into the Arduino. Depending on the resistor value you may need to add some transistor to drive the other pins (cathodes) on the display. Lower value resistors means a brighter display, but too much current for the Arduino to drive all 8 leds of a digit at the same time. 

1k resistors, would mean about 3mA of current per segment. So if all segments are on in one digit, that would be 8*3, so 24mA. Which is approaching the maximum current an Arduino pin can source.