Why not download GIMP? Much easier if you ask me.
He's not downloading GIMP because he's downloading Paint.NET.
Use the wand, click on the areas you want transparent. Hit the delete key and it's transparent. If the image needs to be resized at all (for example, it's 400px and you make it your avatar) it isn't going to be transparent. Resize it, then transparent-ize it.
Save it as a .png or .gif, and be careful not to save it as .pdn.