As Mongolia is a landlocked country between Russia and China, there are two principal ways to get to Mongolia : via air or land. Flights to and from Ulaanbaatar, operated by national carrier MIAT(Mongolian Airlines) as well as international carriers such as Turkish Airlines, Korea Air, Air China, are available all year round. The Trans-Mongolian Railway connects Moscow and Beijing through Mongolia and its capital Ulaanbaatar. The Mongolian railway runs to Beijing, Ulan-Ude and Irkutsk. Traveling to Mongolia by private car is possible.
BY AIR
Flying could be the only way to reach Mongolia for a lot of people, especially from the US, Australia and most part of Europe. There are few direct flights to Mongolia's capital Ulaanbaatar - from Berlin, Beijing, and Seoul. Thus, having one or two stops en route to Mongolia is not something abnormal. The flights could be expensive due to limited number of carriers. Tickets are often sold out or much more expensive during the peak season (July-August), so make sure to book the tickets in advance.
Airport
The Chinggis Khaan airport in Ulaanbaatar, whose code is ULN, is currently the main international airport of Mongolia. A new airport, around 50km south to Ulaanbaatar, is expected to start operating from July, 2020. It will inherit the old airport's name. The new airport is designed with a capacity of 3 million passengers per year, and has sufficient space for a possible future expansion, making it potentially capable of serving twelve million passengers annually. In contrast, the current airport is capable of serving 900,000 passengers per year.
Airlines
Major air carriers are MIAT(Mongolian Airlines), Aeroflot, Korea Air, Air China, Asiana Airlines, and Turkish Airlines. Other smaller local airlines are Eznis Airways and Hunnu Air.
Aside from international flights to big cities such as Istanbul, Moscow, Beijing, Seoul, Hong Kong, and Berlin, there are regional flights to/from smaller destinations in Russia. China, and Kyrgyzstan. These include flights from/to Manzhouli, Erlian, Altai, Hoh-hot, Irkutsk, and Dongshan.
Transit
Since there are few direct flights to Ulaanbaatar, one will most likely have couple of stops en route. Be ready to transit in on of these airports: Beijing International Airport (PEK), South Korea's Incheon International Airport (ICN), Moscow's Sheremetyevo International Airport (SVO) and Istanbul's Ataturk Airport (IST).
BY LAND
Besides the Chinggis Khaan airport, Mongolia has over 20 land border-crossing points with both Russia and China. However most of them are not available for third-country travelers. The main border crossing with China open for foreign tourists is at Zamiin-Uud and Erlian. Whereas the main border crossings with Russia are Naushki- Sukhbaatar (for train) and Khyagta-Altanbulag(for vehicles).
Trains to & from Mongolia
Spanning a ridiculous length of 9289 km, The Trans-Siberan Railway is the longest and yet the most famous railway line in the world. One of the branches on the line is the Trans-Mongolian, linking the Chinese railway to the Trans-Siberian. The Trans-Mongolian line was built between 1949-1961, from the north to Ulaanbaatar, and from there to China. Take a look at the train schedules below.
Schedules change every year. Services increase in summer and decrease in winter.
-via Lonely Planet
BY CAR
It is getting quite a trend among travelers to travel with their own vehicles. First thing first, you must inform the tax authorities and the border troops in advance at any of the border crossing in the country.
Then, as long as you have all the valid documents(driving license, ownership records, insurance), it is not a big deal to enter Mongolia with your car. All you need to do is fill a declaration form. But bear in mind that Mongolian road could be very bumpy at times, thus you need to make sure your vehicle is in good shape. Once you are in Mongolia, it will be hard to find auto-services or petrol stations outside the towns(which are 200-300km away from each other). So, it will be wise to take these tips into consideration.