It looks like the other posts have directly answered the question here. Just thought I'd also mention taking a look at opencores.com... This site has open source HDL (Verilog and VHDL) implementations of working hardware...
You still require the vendor's tool to actually program the FPGA device (as mentioned by others), but companies like Altera provide free web edition tools (Quartus II web-edition) which is free to download. The free versions don't have all the bells and whistles, but it will be enough to get you going for some of their lower-mid range devices (Cyclone II, III, Stratix II)... Pretty cheap chips sometimes (US$80 or so for the Cyclone III 40k gate FPGA).
-So putting it all together, go to the FPGA vendor's website, check out Cyclone series FPGAs and make a purchase for what you need.
-Set up your environment with the free web-edition (Altera.. I am not sure about Xilinx)
-Grab a complete simple project from opencores.com
-Program the FPGA and test it (simulation is separate software tool from current Quartus II tool version)
Note, you may need to buy a vendor-specific programmer (JTAG pins)... A good place to check out some basic projects may be at sparkfun.com.
Happy developing!
Check out a list of ready-to-use boards at http://www.fpga-faq.com/FPGA_Boards.shtml.