At the bottom of that page there is a couple of textbooks on digital design. One of them you can find as a free pdf. These books provide an easy to follow intro with examples, intended for this board.

You can get into FPGA just like you get into any other hobby - start with something simple, then progress to something complex, one step at a time.

For example, start with implementing an adder. By implementing I mean writing a description of the adder in a hardware description language. The description can be structural (describe the circuit which does the addition), or functional (describe the desired output of the circuit given specific inputs). Then you load that description into the board, and your circuit will created there from logic gates. This is not much different from regular programming (actually simpler, because you're much closer to hardware, so you can see better what your "program" is doing).

a + b

Best go with structural if you want to actually learn something. This book ( http://www.amazon.com/The-Elements-Computing-Systems-Princip... ) is very good and I think still stands as the best introduction to this type of stuff I've seen. It's also presented in a straight forward enough way that it's good enough self-study for anyone with some programming experience.

Note, however, that it does not use actual hardware, nor a real hardware description language - it's just a hardware simulator (this might be important for someone who's interested in FPGA per se).

Instead, there are discount vendors that will sell older chips (generally 2-3 generations behind the curve) for cheap. The names to watch are Digilent for Xilinx and Terasic for Altera.

I tend to prefer Xilinx stuff. I don't really have the time to write a more detailed reply, but you can browse around here [1]. Get something with lots of ports, or you won't be able to make anything interesting without a lot of pain (where interesting means "I want to hear/see/communicate-to another-computer my results"). The Zynq boards also come with an ARM processor that can talk to the FPGA fabric.

[1]: http://www.digilentinc.com/Products/Catalog.cfm?NavPath=2,40...