When I was a boy I learned about a tribe of natives (Lipan Apache) that had an initiation into manhood which involved plucking a hair from the tail of a live deer. These people had developed a mode of stealth that allowed them to walk right up to deer–head on–without the deer sensing their presence or noticing their advance. I adopted the technique for moving through the woods silently, but never to the point where I could stealthily touch a deer.
I'll skip the masking your scent and disguising your appearance parts and just give you the silent walking part.
First of all, you must have good balance, so take a semi-squat stance to lower you body weight. With each step, you will balance on one foot, while you test the ground ahead of you with the smallest toe of your other foot. You want to plant your foot where it isn't going to make any noise, first touch the ground with your small toe, using it to part the grass or move leaves, then gently rock onto your lateral arch down to your heel as you shift your weight onto your forward foot and flatten it out onto the ground, the last part of your foot to touch the ground is your big toe. Complete the step by transferring all your weight to your forward foot, then feel ahead with the other.
The deer touchers did this very slow, averaging about 80 seconds per step, in a breeze they could rock with the grass and branches and go about 60 seconds a step. The super slow speeds were so the deer wouldn't register them moving, even if they were staring straight in their direction.
When nothing's watching you you can move quickly through the woods stepping this way, just touch with your small toe first and ease into each step, when you get good you tend to glide more than you stride. The part to practice is making contact with the ground without making a crunch, it's easy to do on a path, but harder to do when moving through the bush.
As far as what clothes and shoes to wear: the deer touchers went barefoot and wore nothing but a loincloth and ash from a fire, but any soft soled shoe will work for foot wear, toeshoes would be the best. For clothing you don't want to wear anything synthetic, nylon and polyester make that whishing sound when you walk. Soft cotton or wool is best for moving silently, think ninja knickers, light and breathable.