When Jans crossed the border the border guards asked for a ticket, so Rozwal's method would not have worked. Though this may be because Jans had showed up the previous afternoon so the guards may have been expecting a hitchhiker.
There seems to be no passenger cars crossing the border, just trucks and buses.
Bus tickets to the first Russian town after the border cost 140 Yuan in April 2015. The bus station is a a brown building with a large clock on it, a little bit to the east of the big lake on the road to the border, about three kilometers before the border itself. Tickets can be bought at a ticket booth on the second floor which opens at 6:30 and the first bus leaves a little before 07:00 AM. They accept both Yuan and Ruble. Apparently there are no buses in the afternoon, though you might want to check this out for yourself.
To get to the customs area by yourself take the main road out of town, then take the road that heads left about one kilometer before the actual border, this will through a special tourist zone to the customs area.