How to shoulder a bike? In a previous question it was explained to me that no cables pass under the top tube of my Specialized Hardrock, so that the bike is easy to shoulder. 

Well, it isn't. The top tube is quite thin (V-shaped) and the only way I can pull this off for more than a couple of minutes is to place the bike exactly over the shoulder strap of my backpack. But maybe I am doing it wrong.

How to shoulder an MTB? Should the bike be parallel to the ground or vertical, or tilted? Are there some bike designs that are aimed to be carried (besides all light bikes) - maybe the cyclo-cross bikes?  Are there any suitable preparations before leaving to a journey in the high mountains, where one will be passing very difficult terrain with the bike on the back?*

Very difficult for someone carrying a bulky bicycle and a backpack with food, at least. Summer weather, maybe muddy.  About 2000 meters height. Crags and plenty of options to trip and fall.
I ride a lot of trails where it is almost impossible to ride up and sometimes not even practical to push the bike up, and it is easier to carry. I've got a full suspension mountain bike with no space inside of the triangle, so it is not possible to shoulder it. And carry a bike on my back, rather than on a shoulder. Bottom tube is resting on my shoulders with rear wheel on right from my head and front wheel on left from my head. 

Like that:



It helps if you have a backpack, as the bottom tube rests on it. After some practice you can have both of your hands free, while bike comfortably sits on pack. This way bike does not get in your way and you can hike quite a big distances.

UPD: This position is not the quickest to put the bike up, but I find it the most comfortable when climbing. To get the bike up, stand on non-chain side of a bike, place left pedal (closes to you) in the lowest position, grab with one hand the left crank and fork stantion with the other hand. Lift the bike over your head and on your shoulder/backpack.