That's going to be difficult. You're pretty limited.
http://pcpartpicker.com/p/23Gz5 That is not the cheapest you can go, and it does not include an OS, but it will be about the minimum you need for a decent build. It has an APU because you don't really need a video card, and it's a good processor. Then you have 4gb of 1866 RAM because APUs benefit quite a bit from faster RAM. The case includes a power supply, and then you have a disc drive and motherboard, both going pretty cheap, though it won;t matter.