We have all heard of the Trans-Siberian Railway, the longest train journey in the world. It runs from Moscow to Vladivostok, Russia, and takes 7 days. The Trans-Mongolian, on the other hand, runs from Moscow to Beijing via Mongolia, and takes about 5 1/2 days. Click the map above to enlarge to get a perspective. The Trans-Mongolian does link with the Trans-Siberian line, so that's why you sometimes hear the Moscow-Beijing route referred to as the Trans-Siberian Railway.
Some people take the Trans-Mongolian Railway, starting in Moscow. Here is a great video by an Italian tourist who did take the train in Moscow. Others, who start out traveling in Asia first, perhaps jump on the train in Beijing and take it to Moscow. The 5 1/2 days would be the total if you did the entire trip without getting off the train. However, travelers who desire to explore Mongolia and Siberia, usually do a stopover in Ulaanbaatar - the capital of Mongolia - to see Genghis Khan's homeland and stay in a yurt with a Mongolian family. They also get off near Lake Baikal for a camping experience, and then hit a couple of larger cities, like Novosibirsk or perhaps Yekaterinburg, the city where the Romanovs were murdered. Of course, if it's winter, your itinerary and activities would likely be very different. I would prefer the warmer months, but some people say that a winter train ride through Siberia is amazing.
Here's a Smithsonian article about the train experience across Siberia. Also, here's a link to Monkey Shrine, a business that specializes in helping travelers plan their Trans-Mongolian/Trans-Siberian experience. And, if you want to read up on another post writeup I did on the Trans-Siberian Railway, click here. Finally, if you like movies, check out this thriller.