Some of the people answering here seem to not understand that you want something for mobile, not IE, Firefox, etc. They also don't seem to read very well where you said "website", not "mobile app". However, I believe I have read your question properly.
There's extremely high odds that you'll probably also want this for iPhone, so I'll answer this for iPhone and Android as well.
For iPhone, it's as simple as using this script:
http://code.google.com/p/mobile-bookmark-bubble/
For Android, it's not so pretty, unfortunately. You'll have to make a button or hyperlink that redirects to an instructions page on your site. The instructions will tell web visitors to do "Settings > More > Add Shortcut to Home" and hope they "get it".
One option for Android is that you can fork mobile-bookmark-bubble, make it load at the bottom of the page without the bottom triangle, and make it read, "Click the Settings button > More > Add Shortcut to Home". As well, you might want to put the 2 bars icon of what the Settings button looks like right next to "Settings button".
As for how to customize the icon that gets created, I'm still researching that and will update this answer when I find out.
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