It's easy to see how the toad would have something to do with luck and making money, but have you ever wondered what's the story behind the toad and why, upon closer inspection, does it have only three legs.
The toad comes from the ancient Chinese story, "Liu Hai Teasing the Golden Toad." Liu Hai one of a handful Chinese deities of money and wealth. He is often portrayed adorned with a string of gold coins and accompanied by a three-legged toad. In one version of the story, Liu Hai and the toad are friends; whenever the toad gets trapped in a well, Liu Hai uses a line baited with gold to fish it out. In another version, the toad is an evil monster who lived in a deep pool and terrorized villagers with its noxious fumes; Liu Hai exploits the toad's greed by using a line of gold coins to catch and destroy it. Regardless of the version, Liu Hai and his toad have become popular symbols of prosperity and wealth in Chinese folklore and history (nowadays the latter more than the former).
If you happen to find yourself in Hong Kong, be sure to check out the exhibition "Cruising the Universe: Fantastic Animals in the Arts of China" at the Hong Kong Museum of Art. The collection features some interesting works depicting Liu Hai and the three-legged toad, among other things. Here are some of the pieces you'll see in the exhibition (they look much, much better in person, of course).