The only direct flight between Tokyo and Ulaanbaatar is by MIAT. According to MIAT, they fly Monday, Wednesday, Friday, Saturday and Sunday in winter.  The flight from and to Tokyo will arrive and leave Terminal 1, Narita Airport.
There are several ways to get to central Tokyo. But it will approximately take 60-90 minutes from the airport.
There are also flights either through Seoul or through Beijing with Korean Airline and Air China. 
The time table for MIAT:
The time table for Korean Airlines:
The time table for Air China: