I use gimp 2.6.
I add another layer, and then trace over what I want to use and then delete the base layer and fill in the traced line[inside the lines] with white and then color it in. The image should be transparent when you delete the base layer and when you color it in within the lines of the second layer, it should be transparent already. Then save it as gif. and Bam. Also, when uploading it, you'll see the background is black with the tiny view, but don't worry. if you click it, it should be viewed as transparent.

On Gimp or Photoshop, delete the whte background when you make it, so you can see the grey/whte checkers. The save as a gif. If you use something else, I'm sorry but I don't know.

Okay, heres a easy way. If you want a transparent background, go to paint, paint what you want to be transparent ONE SOILID COLOR
ONE SOLID COLOR
Go to lunar pic, somewhere there is a "transparent" option, and you'll click on the color you chose, and then save it on your computer.

Same as Demeter. I don't usually animate, but GIF Is specialized for animations ^^

Save them as Gif, i once tried with PNG and they look like black background and they won't work the best way for me is gif

I'm sure there are similar questions, but you need a program such as photoshop or gimp to make this work. Even photofiltre works, but I personally don't like the results it gives. Anyway, you need to erase the background and make sure the background is transparent. Save the image as gif or PNG.