The most convenient way of travel between mongolian and chinese capitals is by railroad. Being an international part it can be expensive and/or not possible to book it over the internet.
This article explains how to manage the journey on budget.
First, buy train ticket only to Zamiin-Uud. It's the last station on the mongolian side of the border. Trains in Mongolia are very cheap. It cost me 10,600 MNT. There is at least one train per day. It leaves UB at 5:30 pm all days except friday. On friday it leaves on 4:30 pm. If everything goes by the plan you'll be in Zamiin-Uud after 14 hours - around 7:30 am.
When arriving to Zamiin-Uud you have to somehow get to Erlian train station on chinese side of the border. Erlian can be spelled also as Erenhot on some maps. It's not possible to cross the border on foot. When walking out of the station you'll already see busses on a parking lot. They cost 15,000 MNT. But there will also be taxis or just some random people offering you a ride. You have to negotiate because the initial price can be as high as 45,000 MNT, but if you show the driver that you know what the expected price is you can easily negotiate to 10,000 MNT. I even heard stories about people getting a ride for 8000 MNT.
Before geting in a car make sure they will take you all the way to Erlian train station. Most of the people dealing with this bussines speaks english good enough for basic communication.
At Erlian just walk straight in to the ticket office. It is well marked in english. Keep in mind that time in China is minus one hour in comparison with Mongolia. That gives you one extra hour :)
You can check chinese train timetables using websites like ctrip.com or chinahighlights.com and even book tickets in advance. There should be a direct train from Erlian to Beijing, but at the time of my trip it was unavailable. So I bought a train ticket to Jining South and from there further to Beijing. Taking the cheapest tickets it meant I had to sit. To Jining South cost me 50.50 RMB and took me 4 hours. After that I had some time to strech my legs go around Jining for couple of hours. Then I took a train to Beijing, which cost me 53.50 RMB and needed 6 hours to get there.
1. Take a train to Zamiin-Uud (10,600 MNT, daily trains at 5:30pm, 4:40pm on fridays)
2. Take a bus or taxi from parking lot infront of railway station (bus: 15,000 MNT, taxi: negotiate to 10,000 MNT)
3. Take a train directly to Beijing if available
3. Take at rain to Jining South (50.50 RMB, 4h)
4. Take a train to Beijing (53.50 RMB, 6h)