PXE Boot Process
1. PXE client boots up, starts up PXE boot ROM.
2. The PXE boot ROM sends a DHCP request.
3. The responding DHCP request (should) contain an additional DHCP option, the "filename" options. (This is why the average hardware router won't work. You can't specify the needed options.)
4. The PXE client attempts to download the file specified over TFTP. (If not specified, the client tries to connect to the computer that gave it the DHCP lease. If the "next-server" param is specified, it will instead attempt to download the file off of that server. )
5. If the PXE client downloads the file, it then executes this file and from there PXE is out of the picture. That's the entire PXE process.
6. If any of the above steps fail, the computer should continue on with the boot process.