The first thing you do is ask Google for a datasheet. It tells you: http://www.robotshop.com/media/files/pdf/datasheet-com-09483.pdf
Then you can read the datasheet and find the pin diagram:
That tells you that it is a Common Anode LED display - which means that for each digit all the Anodes (positive pins) of the LEDs are wired together.
Further, all the cathode (negative) pins of the LEDs for the same segments across the digits are connected (that is the cathode for segment A on digit 1 is connected to the cathode for segment A on digit 2, digit 3 and digit 4, etc).
From that you can then infer that you need to provide current for each digit in turn through its common anode pin, and sink current from the segments you want to have lit for the digit that is currently having its current sourced.
The diagram also shows you which pin on the display is for what function - the common anodes are pins 9, 10, 12 and 13, with pin 11 the common anode for the extra dots.
The datasheet also tells you which pin is pin 1 - in this case the one in the bottom left when you have the display facing you and the numbers the right way up. The pins count anti-clockwise from there, so 2 is to its right and 13 is above it.
By the sounds of it though you may not have the same display as in that datasheet. If your display lacks the extra dots then it may not have the LEDs on pin 11, and pin 12-13 may be moved down one, so you have 4 commons on 9, 10, 11 and 12 with no pin 13.
So the four digit select pins in your program are wired to pins 9, 10, 12 and 13, and the segment select pins connect to pins 1, 2, 3, 4, 5, 6, and 7. Don't forget the resistors on all the segment pins to limit the LED current or you will damage the Arduino.
You can do some manual testing of the display by using two wires and a resistor (say 1KΩ). Connect the resistor to +5V, and one wire to the other end of the resistor. The other wire you connect to ground.
You then take the loose ends of the wires and try probing pins. Start with the 5V wire touching pin 9 and connect the other one in turn to pins 1-8 to see if the first digit's segments light up. Repeat with the 5V wire on pins 10-12.
If this (http://mklec.com/displays/7-segment-4-digit-12-pin-common-anode-display) is indeed the same display as yours you can ignore the numbers I mention above and work from the pin numbers on that page. The same principle applies though, just the pin numberings are different.