"GNU Image Manipulation Program"
First, note that the image has to be either GIF or PNG. If your image is JPeG or something else, convert it using The GIMP by opening it, then doing Save As....
Next, perform these steps with the image loaded into The GIMP. When you perform these steps, don't fret that you fail to see the application do anything obvious.
Note that if you've got something pretty white on a white background (could be another color you're selecting, so this doesn't apply only to white), the transparency may obliterate it in an undesired way. To fix this, use the paint can tool to change the color of the background before selecting By Color. If you have trouble with this working, please see the solution below.
The paint can might not be too discriminating. It dumps paint to re-color places in the image and it will often leak out over similar colors. This is especially frustrating when you're trying to do some transparency work.
To fix this, leave selected Fill similar colors, but select Sample merged and play with the Threshold setting: the lower the number, the more discriminating the effect.
Read about this here. Or follow these brief steps.