Welcome!
Make an animated Icon is really easy,
you need a paint program - that can make layer AND folder, and can save your file as PSD (photoshop file) ( okay the folder aren´t necessary, but it makes it easier)
like Sai, Krita, Gimp, .... I use sai
And a Programm that can make Gif´s - I use Gimp
(Okay, if you use a program to paint, that can create gif, you don´t psd files)
If you to Use it as Icon here on Da, it has to be 50 x 50 pixel and not more than 15 kb.
An Advice: use a Base, if you have never done this bevor. It just 50 x 50, its extremely small. It´s a bit like you have to learn how to draw again.