If the image is anything other than a .jpg or .jpeg file, you have to make it that. 
To do so, click on "Colors / Increase color depth / 16 million colors (24 bit)". 
You have to first promote the image to a layer. 
You do that by clicking on "Layers / Promote to Layer".
Click on the Magic Wand. 
Click on the "Toggle Tool Options Window". 
At the first tab, you probably need to change the tolerance.  The average is about 15, but it could be much  higher if you are getting white outlines around your graphic still.  The higher the number here, the closer the  magic wand gets to the image, thus illiminating more and more white around the edges.  And the opposite goes if you need the wand farther away, because it's cropping off too much of the image. 

Now set FEATHER to either 1 or 2. 
So now, with the magic wand still activated, left click in the space around the graphic, but not on the graphic itself.
Now all you do is press "Delete" on your keyboard.
Your background should now be transparent.
Keep on clicking in any leftover white areas and deleting if need be.
Or if you hold down the shift key on your keyboard, you can click in all of the white areas and delete them.

You may not realize that the background is indeed transparent because you may not know your transparency scheme. 
To check that, click on "File  / Preferences / General Program Preferences". 
Click on the Transparency tab.
You will see in the preview box your transparency scheme.
You can change it to what you want. 
Personally, I have it all one color...a real pale blue color.
OK the box when done.
 
~Summer °Ü°