The Ukrainian troops seem to be carrying older AKS74's with the triangle folding stocks. The Russians, of course, are using the AK74M with the upgraded polymer stocks. In the photo immediately above this paragraph, the soldier on the left looks to have something from the AK-100 series, what with the Picatinny rails. The photo below (source) also shows a Russian using an AK74M upgraded with a quad-rail set up on the front stock.
Both the AKS-74 and the AK74M both use a folding stock where the sling swivel is positioned on the right when the stock is open, but on the left when the stock is folded. The front sling attachment is on the left. Thus, simply slinging the weapon over the shoulder only works well when the stock is folded.
The photos show two basic slinging techniques being used by both the Ukrainian and Russian soldiers. Both involve slinging the rifle around the neck. Using both attachment points, the sling simply goes around the neck. While this is an okay method of carry, you have to be cognizant that the front of the rifle is not very maneuverable. That is, you have to turn your body more when confronting a threat (or unsling the rifle) to get the muzzle on point. The soldiers using this method are carrying unloaded rifles (no magazines).
The second method is a single-point method, using the sling attachment on the stock. As you can see from the photos, the front of the sling is simply clipped onto the rear sling attachment, and, again, the rifle is slung from the neck. Obviously, since it only involves moving the clip point, it would be easy to transition the sling from single point to two point. The soldiers are also wearing the rifle high up so it is not banging against your leg (or into your groin)--a common problem with the set up of most American single-point set ups I've seen.
I would also note that none of the photos show troops using a leather sling.
(Updated 3/4/2014)--Changed my orientation from that of looking at the photos to that of a person handling the weapons. Thus, some of the "lefts" and "rights" have been reversed.