As has been said, pick up your feet (no shuffling) and walk slowly. To that I would add I use a turkey diaphragm call. Move a little, then give a few putts or clucks. I have bumped deer, then clucked a few times and had them stop and resume feeding. I haven't killed one that way yet, but I have gotten inside 20 yards on some that I just chose not to shoot. One was an old slick-head! That's a trick in my book. I was holding out for a buck, so I didn't shoot her. I just wanted to see how close I could get. I was out in the open, but by just taking a step or two, then stopping to give some soft putts I got to about 15 yards.
I finally got tired of playing with her and waved my arms...scared the crap out of her when I did that...fun!
I may give it a try again this year, but I just love the view from a tree stand, so I'm not giving that up any time soon.