You cross the reins under their chin, then you only hold the reins in one hand. When you get ready to turn, you move that hand towards the way you want to turn. So if you're wanting to go left and you have both reins in your right hand, you move your right hand towards their left shoulder which pulls on the right rein, which runs down the right side of their neck putting slight pressure there first before going under the chin and pulling on the left side of the bit. It's supposed to be a pre-stimulus kind of thing where they're supposed to eventually realize that the pressure on the opposite side of the neck is a precursor of pressure being put on the bit so they eventually respond to the neck pressure as soon as they feel it. But it only works if you just use one hand. If you get in a jam and try to direct-rein them with the reins crossed that way, you'll confuse the hell out of them. Been there done that. I felt like a total klutz/moron. It definately takes some getting used to for both horse and rider.
I tried it not too long ago when I borrowed Blade back from Carolyn and she had been riding him that way trying to teach him to neck rein and wanted me to do it too while I had him. It was very awkward at first because I couldn't figure out what to do with my hands, but I finally got the hang of it. It doesn't take them too long to pick it up either.
Ah - good tip. Seems like something to do in arena when specifically working on that... I wouldn't want to do that on trail... for those 'bind' reasons you mention ;~D
Hair, I dunno know, the trail might be the best place to train neck reining. A little bit of weaving around the trees, would be good practice....

We teach horses to neck rein with the reins in their normal position. We just use leg pressure and put the off rein against their neck. That way we aren't working on an accident by having the reins crossed if we need them. The horse learns to follow his head with the direct rein, move with the leg pressure and the neck pressure. All of it means turn and eventually any one of the three means turn. Working on this in the sage brush is good practice and training because they have to turn :) or plow through a 3' prickly sage brush.