For use in some of my presentation slides, I hope to edit some of my images with The GIMP so that one (or more) side(s) will fade into transparency. How do I do this in GIMP?
You could flatten all the layers, then add a layer mask, and paint a white-to-black gradient on the mask. The black part will be transparent.
If you wanted all sides to fade to transparency, you could start off with a black layer mask, then draw a white rectangle inside it, and apply a blur. In any case, I think starting off with a layer mask is what you want.