I shot a deer while stillhunting yesterday. The key is to move slow. When the squirrels are oblivious to you, that's about slow enough. You should be standing still much more than you are moving. Stillhunt into the wind or across the wind. You also have to look at everything more than once. Angles change enough to expose a deer you could not see in only a step or two. Be ready to see deer bedded, and not just walking or standing. Mine was bedded when I shot him at about 40-45 yards. He saw me at the last second, but he hesitated one second too long.
Don't be too concerned with making noise if the leaves are dry. Everything out there makes noise. It's more of a rhythm thing. If your cadence sounds like a person walking you will spook game. If you snap a twig be sure to stop and get ready to see a deer stand up. Watch your backtrail, as deer will sometimes let you pass at close range and sneak out behind you.