Thank you to Rob LeFebvre at Cult of Mac.
First, use Preview to open up an image that has a lot of white space in the background. In the upper right hand corner of the Preview window, there’s an editing button that sort of looks like a highlighter in a square box. This will drop down the editing toolbar in Preview.
Now, the fourth icon from the right in that toolbar is usually set to a rectangular selection box. Click on that, and you’ll get a drop down menu that shows the other editing selectors, including Instant Alpha, which looks a lot like a magic wand.
Take your cursor now and click and drag in any of the white space in the background of your image. The space will turn red while you’re dragging, and then become a standard selection box when you let go of the mouse or trackpad. You’ll then be asked if you want to convert the image to PNG, if it isn’t one already. Do so.
Then, hit the Delete button on your keyboard to get rid of that selected section. Do the same for the rest of the whitespace you want to delete. When you’re finished, save your effort, either as the PNG you saved it as already, or as a GIF file, the other transparency supporting format.
Now you’ll have a nice transparent image, ready to put onto any other image or website where you want to see the background colors through your new image. Have fun!