I decided to pop one of my Thermaltake Riing 14 RGB fans open and look at what leds are inside. Here's a photo of what it looks like with it open.
They aren't even glued in. If you want, you could swap them out for other leds. It might even be possible to swap the leds in the non-rgb version of these fans to actual rgb leds if they haven't changed anything. The wires are color coded for our convience: White = 5V, Red, Green, and Blue. I cut the wires down as close to the fan motor as possible then extended the wires by soldering extra wire onto them.
Then, I followed the tutorial on the Adafruit website for hooking up a simple rgb led. These leds are the common annode type so don't forget to use the common annode edits. You have to plug the +5V into the 5V plug on the Arduino, not the ground. The tutorial says to use 270 Ohm resistors, but I'm using 220 Ohm because that's what I had.
There's even some simple code there to show you how it works. You'll have to learn how to code for it, but there's plenty of examples out there so it isn't that bad. Personally, I have a Windows App that controls all my led strips which I coded control of my fans into. I'll do this to all 8 of my fans eventually. Now they'll all be 16.1 million colors instead of 256 and fully software controllable.
(I can't figure out how to embed Youtube videos here so here's a link to it working)
If you're wondering about how to power the actual fan, 4 of the pins are your standard mobo header pins while the 5th pin is the 5V to power the leds. Here's a photo of it running directly from my motherboard. The fan is a PWM fan, so make sure you're using PWM headers.
Looking at the photo above, from the right to the left: Pin 1: Ground Pin 2: 12V Pin 3: Signal, fan rpm Pin 4: PWM signal Pin 5: 5V (for leds, don't need to power fan) I'm using jumpers there to connect, but you can use a extension cable that doesn't have a housing around the male side or you can cut the side off the housing that interferes. If you want, you can rewire it with a 4 pin connector to fit it to your favorite fan controller. You can also just use the fan controller for these fans.