I mean with this is not possible -> if you want to generate HDL to program the FPGA.
Offcourse it is possible to program your computer with serial communication, usb protocol etc to communicate with an external peripheral wich can be an FPGA board like the Spartan 3A starter board... you can also give jtag a try...
The only xilinx board wich you can program is the spartan 3E board.... under license that only fit educational institutes...
try this site: http://pwo.fpga.be/ and search for courseware.... it may help you out