It's a really long process depending on how smooth you want it and the difference of colors. Involves making multiple layers, a layer for each color and letter and using the timeline at the bottom of Photoshop. Something like your avatar would be pretty simple though since it's just a gradient moving left to right.
I'm pretty new to PS myself and I'm sure you could use tweening somehow but not sure.
Here's something to get you started in the right direction. It's not what you want but it'll give you an idea on how to do it.
http://www.youtube.com/watch?v=58P2XG75muI