Back in 2019 a went from Berlin via Slovakia Chop (Hungarian/Slovakian/Ukrainian) border to Odessa and took from there a daily train to Chisinau via Tiraspol. 

From Chisinau i took the direct Nighttrain to Bucharest (with customs/bordercontrol and Boggie change in the Evening. 

Actual its hard to find uptodate Informations as Moldovian Rail (CFM) went bankrupt few months ago. 

Another option is to catch the russian Nighttrains from St.Petersburg/Minsk/Moskau to get to Chisinau or Moldova some of these trains stop in Kiev or Lviv.

Assuming you travel via. Romania you'd be best off taking a bus to Chisinau from the Romanian city Iasi.  Bus station is located right next to its train station. There's a train but it rarely runs which is why I went with a bus (there are several daily departures)

I went Budapest->Iasi via. Cluj-Napoca. Second stretch is a sleeper if you prefer. That would be my recommendation. Book in advance as spots are tight.  Also be sure to spend a night in Iasi, former capital of Moldavia :)