It's the town on the Mongolian side of the sole border crossing into China open to foreigners. You will pass through it if you're travelling between Beijing and Ulaanbaatar as described in Mongolia#From_China. The town on the Chinese side of the border is Erlian
From China, you can cross the border from Erlian as described in Erlian#To_and_from_Mongolia.
To China, instructions are pretty much identical to the above, with the following amendments:
To Ulaanbaatar your best option is by train. Trains leave Zamiin-Uud for Ulaanbaatar on at least a daily basis, as of March 2011 at 17:35 and arrive at 10:00. You can buy tickets for the train from the top floor black glass building to the left of the main train station building as you face it. Left luggage is in the basement of this building.
Getting tickets on the same day can be an issue - later on in the day often only soft sleeper and hard seat are available. At busy times (for instance around the Nadaam) and on days when only one train to Ulaanbaatar runs sometimes soft sleeper sells out as well. It's best to cross the border as early as possible to ensure a bed. If you speak Mongolian, you could also try contacting Anda Tour below who can reserve tickets for you. If you're travelling from Beijing to Ulaanbaatar, you could buy a package from one of the guesthouses in Beijing, but this is probably only worth it around the Naadam.
Prices increased dramatically at the end of 2008 and again for 2011 - it now costs 16,300 MNT (October 2011) for hard sleeper and 40,000 MNT (4/2011) for soft sleeper to UB and takes 16 hours for the slow train at 17:35.
Below is the timetable for trains leaving Zamiin-Uud as of July 2009 (some out of date):
With your back to the station in the rear left of the square there's a building which contains a bank, hotel & restaurant which serves decent food, and a load of eateries around the square.
The beautiful "yellow shop" to the left of the station sells ice cold beer.