As slow as you can stand it. Seriously.

I always try to still-hunt "cross compartment", going over the finger or ridge instead of along the contour.

Take advantage of gusts of wind to cover the noise of your movement (if you are in the woods / deep leaves / thick cover).

Stopping next to a tree is good advice - it can help brace/support your shot and can also help hide your outline.

One final thing, and it may seem like common sense, but always plan to halt your movement in a shooting stance -- if you are right handed, that means left foot forward. I've seen lot's of folks stop with their feet square to their line of movement or even with the "wrong" foot forward.