An old pc that has a built in network card that supports pxe (pre execution environment) boot.
Network for the sort of thin client to connect to the server.
Server that supports pxeboot to push an os such as LTSP, DRBD, Redhat, or maybe MSXP Embedded remote boot.
Screwdriver for removing parts.
Certain old pc's where the bios does not support pxe boot can be made to emulate pxe with software via a boot disk using standard nics. (www.etherboot.org
Free terminal server software.
linux terminal server
Update: I have even used old Apple Mac g3's via netboot as thin clients for LTSP 4.x. Weird seeing old ppc based macs boot from and Intel based machine. Of course you are loading Apple software and not Intel software into the Apple based thin client. There is even software to use the old Sun (now Oracle) thin clients with LTSP, but I never tried it.