For the most part it involves taking existing pictures and modifying them through a graphics program like PhotoShop. The trick is finding the right picture and modifying it, and usually it doesn't involve much work on the part of the creator.

Your first icon is likely created from an existing image that someone drew. It looks like a LiveJournal icon, so there are a lot of people that make those.

The moving icon looks like it was captured by a movie to animated gif convertor and then stringed together into a single animated gif. The gif is then likely modified in size and speed in a animator program like Adobe ImageReady.

The colorbar is likely done by compiling a series of drawings of that character (from Saiyuki I believe, but I forget his name) and then adding different color tones to it through PhotoShop. He likely took each image and increased the values of each color from each image (bringing forth more yellows, reds, blues, and whatnot forward from each image) and then stringing them together into a single image.

My advice is if you really want to try to make images like this is to get yourself a copy of Adobe PhotoShop and start familiarizing yourself with the program. Search for some basic tutorials on how to use the program on-line and then tryi applying them to images that you like. It's fairly easy to do once you get the hang of it.