First, the hardware. I got EVERYTHING from Adafruit.com. We have three primary components: An Arduino, a Wifi shield, and 4 1/4-ring Neopixels. I also got all my bits of wire and solder and sundry components from Adafruit as well.
Let's look at the hardware first. Here's what we're building. Note in this diagram the LED ring depicted is NOT the 60 element ring, but I think the idea is pretty clear.
Following the instructions from Adafruit, solder together the 4 Neopixel 1/4-ring pieces into a single ring. http://www.adafruit.com/products/1768. I'll just re-emphasize some of the more salient parts of this. While you DO want all four joints of your ring to have the 5V and ground connections soldered, make sure you DON'T solder together the data pads of the final joint -- you only want that data signal going in one side. I chose to have my power, ground, and data wires all leading off the same joint. I don't think it's necessary, but it looks cleaner to me.
After assembling the ring, it's a good idea to connect your ring to the Arduino and fire up a sketch to exercise the ring. You want to be sure that all the LEDs light as expected, otherwise when stuff doesn't work later you won't know if it's your hardware or your software. That's no fun. Your pre-requisite task for this is to have downloaded and installed the Arduino IDE and downloaded the Neopixel libraries from Adafruit, available on GitHub. There are plenty of tutorials available to walk you through how to use this software, so I won't bother here. I discovered when I first ran the example sketches that only half my ring lit up, with a couple of odd LEDs here and there turned on for the remainder of the ring. Turns out I had a cold solder joint on the data pads between the second and third rings, so signal wasn't making it through. Better to find these problems now than later!
Some additional notes: I also followed the precautions noted by Adafruit to place a large capacitor across the power supply and put a small resistor inline with the data connection. They know more than me about electronics, so I did it. It works.
Your next step is assemble the WiFi shield, which is nothing more than soldering on the headers so you can attach the shield to the Arduino. As with the ring, I fired up example sketches to be sure that the WiFi shield was working properly. Below is a pic showing the wired up hardware with a trivial Aruduino sketch lighting up the ring with simple colors.
At this point, we have hardware. At the end of this series of posts, I'll provide a complete parts list for what's been built. Now we're ready to write some code to make the hardware do something...