The video above is entitled "The Fox Walk--How To Walk Silently Through The Woods" and from Survival Lilly. It demonstrates a stealthy way of stepping when stalking. She notes that this is a good method to use for hunting, or for escape and evasion, but I would also note that it is also useful for the nature lover: sometimes, to enjoy nature, you just need to be quiet so you can hear the rustle as the wind moves through the branches of trees or grass, the chatter of a chipmunk, or the lazy buzz of flies or bees around the flowers.
I have never considered myself to be very skilled in walking silently--at least, not to the level of skill my father or older brothers could move when hunting--but am constantly shocked at how noisy many (most?) people can be. Many people smack their feet down onto the ground rather than placing their feet onto the ground. As a consequence, they can sound like a herd of elephants, even when walking on a bare trail.