Here is a picture of a common tri-color (red, green, blue) led: (click to enlarge)
In the following example: (click to enlarge)
+5 volts is applied on pin 2 of the led (the longest one) and ground is applied on Red (pin 1), Green (pin 4), Blue (pin 3), this will make them light up.
Please note that the schematic provided earlier will only work if you want to light one color at a time, if you want to light more than one color you will need resistors before the ground on each channel.
The color pins can also be grounded via a micro controller, transistor, mosfet, etc. You can also mix the led colors and intensity (using PWM) to make virtually any color of the visual spectrum.