I've been wondering, how do I remove white space from images with GIMP? I've tried everything, and it still shows up.

I had it colored as a black background before, and when I posted it here, it comes out white.
I noticed that both Sky and landbeforetimelover have images in their avatar/signatures that way, such as these:


I've had a few images that I would want like the two above for avatars on GOF.
Can someone post steps of how do this if possible?