There is a brand new comfortable Swiss train running from Minsk to Zaslavl. Please note that the railway station of Zaslavl is called "Belarus".
For our journey to Zaslavl which took about half an hour by the modern train we bought the ticket the previous day which is not really necessary though. It cost in August 2011 exactly 2000 BYR. Please note that you need to buy your ticket either at the pregorodnye kassy (as you enter the main station building in Minsk to your right, or outside just by the platform which is to the right of the main building). On the way back we used an old style electrichka train which cost 1550 BYR.
In the modern train you even find a toilet.
There are toilets at Belarus station in a separate building to the side of the main station building. Come prepared with toilet paper and don't expect any doors at the cubicles of these hole in the ground variety toilets (men and women have separate entrances). Also there is no hand washing facility, so wet wipes may be a good idea.
We saw one of the infrequent buses at the bus stop "School no. 1". This bus stop is located on ul. Sovetskaya very close to the town hall in the old part of town.
On the second picture you can see the timetable of the station. The bottom line are the buses to Minsk.
There is another such bus stop at the other end of ul. Sovetskaya in the Mikrorayon 1 with the name of "School no. 2"