One way is to go down the Raspberry Pi route.
Tiny computer, fit it in a tiny case, install XMBC for Raspberry Pi and a 3Tb NAS drive attached to your network.
Use your normal PC to rip your discs to the NAS, and then play them back via XBMC.
Loads of stuff on the web about it.
If you want a proper media centre, able to not just stream but play all your discs, rip discs using the same machine etc. etc. then you're looking at quite a bit more money.
You'll need basically all the bits for a full PC, memory, motherboard, processor, DVD/BluRay drive, media centre case etc. etc. You have a choice of operating systems and media centre software though, from Windows 7 Home Premium and above that comes WITH Windows media centre, Windows 8 with the media centre add on that costs extra, Windows 7 or 8 with XBMC, Plex or other such software or one of the Linux distributions designed for media centre use.