These instructions assume you are using the suggested radio shack Multipurpose PC Board. The first image shows a completed board that can be used for reference.
Take the PC Board, and if you have the red, blue and green sharpies, use the second image on this page as a guide to color in some of the white areas on the top of the board. Given that I have staggered the 3 different colors on the board to make color mixing easier, the reference of having in colored pads on the board is useful, but not strictly necessary.
Using the colors as a guide, attach the 9 LEDs. The center leads are going to be ground, so be sure to solder the flat side of the LED to the long narrow leads. LEDs can only accept electricity in one direction, so if this part is messed up, you will have a bunch of wasted parts.
Connect 4 longer wires (about 5-7 inches long). 3 red ones, and one black one to the base of the board. the black one will attach to one of the 2 long, central leads. Solder on a short black wire to jump across from one of the long central leads to the other, turning both into the ground.
The other 3 wires should be soldered in the central holes of the colored leads at the base of the board. One to red (right side), one to green (left side) and one to blue (right side). Use the picture for reference.
This step will be about completing the blue connections. Fist, solder a red wire that connects the 2 blue pads at the base of the board. on the right side, solder a wire from the blue pad to the 1 blue resistor. On the left side, connect 2 red wires fom the blue pad at the base to the 2 blue resistors
Same as step 4, but with green, and the sides reversed
Same as step 4, but with red
Take the 4 wires hanging from the base of the board. Use the green and blue sharpies to mark the ends of the wire, so that you know which wire goes in which pin on the Arduino. Finally, if you have the shrink tubing, put the wires in the shrink tubing, and hit it with a heat gun, or lighter.