The basic idea behind double screening is pretty simple to grasp.
Since heat travels upward, it stands to reason that two hives stacked one on top of another should be able to "share heat" for the duration of the winter. (They're also sharing queen pheremone which tells the hive that everything's okay, too, but that's aside the point.)
Now, if you simply placed a piece of window screen between the two hives, stacked one on top of another, the lower bees will bite the feet off of any bees from the upper box who land on the screen. But... what if you separated the two hives with a rim? And used two pieces of window screen, one on the top and one on the bottom of the rim, which are separated by about 1/4 inch of space? That way, they'd still share heat, but they couldn't bite at one another! Do you follow?
The upper hive will need to have an entrance, which should be placed opposite the lower hive's entrance, to prevent drifting. Likewise, because of the added moisture of a second hive, you need to have superior ventilation to disperse moist and humid air given off through normal respiration.
The major downside to this method is the weight of (deep) brood boxes and honey supers, which need to be stacked high atop the lower hive. Feeding with a hive top feeder of any sort becomes nearly impossible, due to having to move all the heavy boxes. And spring inspections, needless to say, are tougher also. It should be noted that if any "mechanical" failure of the hive should occur (like a moisture problem, or a wind gust toppling the hive), you'll probably lose both colonies.
In the spring, should both hives survive, you simply separate them and place the upper hive on to it's own bottom board, and provide top covers to the lower hive.
Simple, no?
DS