Both Paint.NET and GIMP are nearly the same when it comes to controls. And luckily for you, I use both.
In Paint.NET, just use the Magic Wand, and select said background. (It might not select the white clouds though, but listen to further instructions.) After selecting the beackground, set the colour to total transparent. (In the advanced colour selection). And Backspace. The selected material will go trans. Reapeat with other colours.
Also, if you can, give me original image if you want me to take a shot.