You can see the Mongolian transportation page.One daily night train leaving at 20:20 from Ulaanbaatar, arriving at 08:00. Four coaches daily, mini-vans and car service from Ulaanbaatar's Dragon coach station West of the town, on Peace avenue. First class train is about USD20. Dining car on the train with Mongolian food, juice, cokes, beer, snacks etc..The third class "common" train is the cheapest way to go to Erdenet: 6 800 MNT. Mini-vans will then drive you from the station to the city centre 8 km from the station for 800 MNT. Coaches go from Ulaanbaatar for 11 000 MNT and can take more for extra luggage.
The highway is paved all the way from Ulaanbaatar, but it is two lane and not well maintained. Some people avoid the car and mini-van services because the drivers tend to drive too fast and there are many accidents.
It is possible to bicycle, but watch out for speeding cars.