I have a short abstract of the Trans-Siberian Railway:
Trans-Siberian railway is the world's longest and the most famous train route that goes through Russia. It crosses the whole continent, starts in Moscow, passes through the European Russia, crosses Urals mountains (which separate Europe and Asia), continues into Siberia's taiga and steppes, and finishes in Vladivostok — the Russian Far East coast on the Pacific Ocean.
The best time to enjoy the journey is between may and October because of the wheather.
It takes more than six days to travel along the whole Trans-Siberian, so it is recommended to make stopovers along the way — like this your trip will be much more interesting also.
After Moscow, I recommend you to stop in:
katerinburg, Ekaterinburg, Novosibirsk, Krasnoyarsk, Irtsk, Baikal Lake, Ula-Ude, Khabarovsk, Vladibostok