In Beijing, the cheapest way to get to the Great Wall in Mutianyu is to take the public bus. Most people I asked, for example at the hostel reception, didn’t know about it, but there is a public bus which goes directly to the Great Wall in Mutianyu and back (however some resources say that it is only operating during tourist peak season).
This bus has the number 936. —According to some comments on this post, the bus number is now 867. The rest should be the same. I don’t know if the bus number has changed or if both buses go directly to the wall now. Please fell free to comment if you know anything about it!— The bus station is near the “Dongzhimen” metro station. However this bus station is not the main bus station right next to the metro station, therefore it is not so easy to find. All the info I found on the net on how to get to the bus station did not help at all and it took me an hour to finally find it by luck. I thought a google map with a flag at the bus station would have been useful. So here it is:
The blue line shows the way from the Dongzhimen metro station to the bus station.
The price for a one way ticket is 16 Yuan(CNY,RMB) (in 2010).
The bus departs from the bus station in Beijing at 07:00, 08:00, 09:00 and goes back to the city from Mutianyu at 14:00, 15:00 and 16:00.
The entry price at Mutianyu is 40 Yuan (25 Yuan for students). If you want to use the cable car then the entry is 60 Yuan (35 Yuan for students).
Altogether this trip to the Great Wall costs 57 Yuan (if you are a student), which is much cheaper than the 300 Yuan they would charge you for a tour at the hostel.
By the way, in China you can always try to get the student discount, which is available at almost all tourist sights. Most of the time the staff didn’t take a closer look at my student id. It could have been a credit card as well.