You can get to Mongolia by train and by air.
By Train:
You can opt Trans-Siberian Railway to reach Mongolia. There are several branches on Trans-Siberian Railway. One branch goes through Mongolia and called The Trans-Mongolian Railway which connects Moscow and Beijing passes through Ulaanbaatar.
From Moscow to Ulaanbaatar, it runs once a week, crossing 5-time zone and it takes 5 days in a distance of 6304 km. and a once in a lifetime amazing experience.,
From Beijing to Ulaanbaatar train runs twice a week and takes about 30 hours in a distance of 1356 km.
By Air:
Domestic air carriers such as MIAT Mongolian Airlines, Aero Mongolia, Hunnu Air as well as international carriers such as Aeroflot, Korean Air, Air China, and Turkish Airlines are offering scheduled services.
Thus Ulaanbaatar can be accessed with regular flights from/to major cities such as Moscow, Berlin, Frankfurt, Beijing, Hong Kong, Singapore, Seoul, Tokyo, Irkutsk Istanbul, and Bishkek. Some additional flights are scheduled to Osaka and Nagoya during the summertime.
Chinggis Khaan International Airport (ULN) is one of two international airports that are located 52 kilometers southwest of the capital city, Ulaanbaatar.
2nd international Choibalsan airport has flights to the Chinese cities of Hailar, Erenhot, and Manzhouli only.