It's said that there are three trains from Beijing Railway Station to Ulan Bator within a week. The Train K23 leaves on Tuesday or Saturday and the Train K3 leaves on Wednesday. The leaving time is at 07:45. The international train ticket need to be booked two months in advance. You should go to Beijing International Hotel to book it as soon as possible.
The Beijing International Hotel is located at 9 Jiangoumen Neidajie, Beijing.

thanks ms evelin
but you didn't aswer my question
how much is the price of the ticket and which is the cheapest way?
thanks so much for your help
waiting for your news
luca

There are two trains running from Beijing to Ulan Bator currently. Both of them have the same ticket fare.
K23--leaving Beijing at 07:45 of every Mon and Tue, arriving at Ulan Bator respectively at 13:15 of Tue and Wed.
K03--leaving Beijing at 07:45 of every Wed, arriving at Ulan Bator at 13:15 of Thu.

Fare: Delux cabin-1227RMB, Soft Sleeper-1056RMB, Hard Sleeper-753RMB.

Hope this helps!