The Moscow to Beijing train 003/004 departs from Yaroslavsky train station in Moscow and arrives 5 days later at Beijing Central station. It is one of the most popular Trans-Siberian and Trans-Mongolian trains for both Russians and foreigners.  It passes through Mongolia and makes a stop in Ulaanbaatar on its way to Beijing.
The train is operated by both Russian and Chinese staff. When the train crosses the border between Mongolia and China, the wheels of the train are changed to a smaller gauge - the whole process takes six hours.
The train has both 1st and 2nd class carriages. First-class cabins have two berths one over the other and a private shower and WC, shared with the compartment next door. Second-class cabins are designed for 4 people and have 2 lower and 2 upper berths.
Meals are not included in the price of tickets but the train has a restaurant car where roubles are accepted when the train is in Russia, RMB when the train is in Mongolia and CNY when the train runs through China.
NOTE: As the train crosses Mongolia on its route you may need to obtain a Mongolian transit visa to travel to China, please check the website of your local Mongolian Consulate.