If the image you are working with is a .jpg file, there will be a white background showing where you would see transparency on the web.
If you are using Photoshop, you can use a number of methods to remove portions of the image you dont want.
You will need to drag this image into a new document that has a "transparent background" and then chose your method of extracting/selecting.
I use the magic wand tool.
You would click the magic wand tool in the area you want to remove -- in this case the white area. You might have to adjust the tolerance levels of the magic wand tool if too much or too little is being selected.
In general, once you have the portion you want removed selected, delete it.