[Updated 8/10/18] p. 54:
Hand-in-hand with changes to the fast-evolving visa regime come developments on the requirement for visitors to register their temporary address within Belarus. This must still be done within five working days of arriving in the country, but it is no longer necessary to complete the two-part migration form that used to be handed out on your plane, train or bus prior to crossing the border.
If staying at a hotel or hostel the process of registration will be completed for you. It only takes a few minutes. You will be handed a small registration certificate. Guard it as you would your passport, because you will need to hand it in when you leave the country.
If staying with relatives, friends or in a private apartment you will need to attend the local Citizenship & Migration office personally (with your host). Take your passport and medical insurance documents with you. After completing the necessary paperwork and paying a modest fee you will be given your certificate of registration for presentation at the border at the end of your trip.