Take a closer look at the device schematic diagram, which I copy below. It will tell you how each of the LEDs are wired. For example, the green LED on the upper-left corner (which I marked with a green circle) has its anode (positive terminal) wired to pin 5, while its cathode (negative terminal) is wired to pin 1. Can you see that?
To light up that LED (green LED on the upper-left corner), you must apply voltage (with limited current), to pins 1 (-) and 5 (+). If you wanted to light up the red LED at the same position instead, you should apply voltage to pins 1 (-) and 20 (+).
To light up all LEDs of a given color, you'll have to connect pins 1, 2, 3, 4, 21, 22, 23 and 24 to the negative terminal of your power supply. These are the LED common anodes. They are called common because they are shared among each pair of red and green LEDs. If you choose to use the red LEDs, you'll also have to wire pins 13 through 20 to your positive supply. On the other hand, if you pick green, you'll wire pins 5 through 12. These are the LED cathodes.
Don't forget to wire a current limiting resistor in series with each LED.