It depends on what direction I'm approaching them from and the mental state of the horse (scared, sleeping, relaxed, etc). If it's from the front and they aren't aggressive or scared I'll walk up to their head and place my palm face down over the top of their nose and slightly over their nostrils where I will then proceed to the pet the neck. From the rear, I'll alert them with a soft noise and place my hand on their body as I walk towards their head. Like I said, it depends greatly on the situation and mental state of the horse. I wouldn't use this tactic on a horse who's scared. If the horse is becoming dangerous, there is no first gentle interaction, there's just me taking charge of the situation without greeting the horse first. If they're scared I approach slowly and cautiously with my hand extended palm up, talking to them as I move towards them.
"And somewhere in the northwoods darkness a creature walks upright. And the best advice you may ever get is: Don't go out at night..."