How to edit an existing image to be transparent
1. Open existing flattened file
Make a copy of your original artwork to work with.
2. Make background into a layer
Double click on the Background in the Layers palette to make it a layer.
Leave layer settings as default and click "OK." You will now have a Layer 0.
3. Select "Magic Wand" tool
You can experiment with the Tolerance, but the default of 32 should work well for solid colors. Make sure Anti-aliased and Contiguous are checked. By checking Contiguous you will not select the white from inside the image when you select the white from the background. If you uncheck it, the white areas inside the image eyes would also be removed.
4. Select your background to be removed
Select the background by clicking within the background area with the Magic Wand.
5. Expand your selection
Before you hit the delete key, expand your selection by 1 pixel. This will eliminate any "haloing" that might be left behind from the Magic Wand. To expand your selection, go to "Select > Modify > Expand" ...
... Enter "1" in the field and click "OK."
Hit the "Delete" key to remove the selection.
7. Preview on dark background
Create a new layer underneath your image layer and fill it with black to expose where anti-aliasing or a "halo" may be present. This will give you an idea as to how your design will look on a black background.
Delete this layer before saving.