I’m surprised that this is being portrayed as some sort of utterly impossible Hollywood-Ninja feat. I’ve personally snuck up on a group of deer to within bowhunting range, which for me was about 30 yards. Your success rate is low, but it can be done.
You have to have a few things going for you. (All, IME, and IMHO.) The wind must be in your face. If they smell you, they’re gone. Period. I’ve never used any covering scents or luring scents, so maybe they change up the equation? Camo is nice, something to break up the outline. The essential piece of it was something to knock down the shine on your face. I used a camo gauze-y face mask, but facepaint would work too. The Schwarzenegger-esque camo from Predator isn’t essential IME in deer hunting. I’m judging this by deer not freaking out when they were looking at me, in face mask, camo long-sleeve shirt and sweats within 30-40 yards. Not moving was the key, not absolutely blending into the background. Now turkey-hunting, OTOH…
Watch where you walk, and if you make noise, don’t do it in a rhythm, for many of the same reasons Herbert cited in Dune. Branches fall in a forest, leaves rustle, but they don’t do it in a “thump-thump-thump” rhythm. Finally, move when the animal’s head is down, like when it’s feeding. Deer can see in a tremendous arc, so be really sure it’s not looking. Ideally, put a terrain feature (like a fold in the ground, small arroyo, that sort of thing) between you and them.
But doing the above—and it’s not like I’m the reincarnation of Natty Bumpo—and I’ve personally walked to within 50 yards of wary deer and closer in camo. As noted by many of you, they’ll tolerate a lot before running, if they don’t smell you. I remember being zoned out with fatigue while deer hunting, stumble-butting up a hill, and hearing a “Woooosh! Woof!”. I looked up, and ~20 feet away was a small buck, who was woofing at me. The next second, he took two leaps and was gone. No idea how long he’d seen this figure stumbling towards him before he decided to make that challenge.
Tree-stands are a much more effective method of hunting than still-hunting, though, IMHO. It just wasn’t an applicable method in the wide-open, low game density region of California where I grew up doing this.