Yes, the "proper" way to use a cane is to hold it with the hand opposite the affected leg; i.e., if you have problems with your left leg you hold the cane in your right hand. And, yes, for most people this results in the desired effect while allowing for a more "normal" gait when you walk. In fact, they addressed this on one episode when House developed shoulder problems because he was using the cane on the "wrong" side (presumably because it disrupts the normal body mechanics involved in walking, but I think they did it just because cane users commented on House using his cane on the "wrong" side). That said, it's more of a "guideline" than anything else, and everyone has to determine for themselves what works best for them. My back problems affect my left leg, and I've found holding the cane in my right hand works best for the most part.
Back to the topic, I'm looking forward to seeing what Risu (and everyone else) comes up with.