I can tell you the general principle and I'll bet you can go from there.
Do you know how to use the tool to select something, like a magic wand or something? Do you know how to adjust the settings so that it selects only a certain color? Cuz what you want to do is select the white portion and then delete it.
The transparency is dependent upon how you save the image. JPG files cannot have transparent backgrounds, so something like GIF is the format you need. I bet when you save the file, there will be options asking how to handle transparency.
Also, you may need to clean up the borders of the black image so that when you insert it onto another color background, it blends correctly.
Here's a page that sort of talks about it, maybe this will help:
http://www.mediacollege.com/adobe/photoshop/transparent/background.htmlhttp://graphicssoft.about.com/od/aboutgraphics/a/bgtransparency.htm