Walk softly watching were you step, about every 25yds Stop, Look and Listen. Keep doing this while stalking. A deer will run off about 25yds, Stop and Watch you, unless it's being pursued by dogs or the hunting pressure is high. If you work the wind, you can do better.
In normal conditions where the habitat is good(Food,Water and Shelter) a deers domain is 1 mile sq.

Watch some videos on Lionesses while they are stalking Gazelles.