Sorry my knowledge is very limited for the DE2 board so I'm not sure what you should do. Since this is part of a lab project you don't need a license (if your school is using Altera devices they may have the license though). If not basically the way it works is that most Altera IP is free to use for academic and experimental usage, and under such a license you just have to have the JTAG connection present if you want to use the design in actual hardware for demonstration purposes.
As for the FFT algorithm my only experience is implementing it in C code on TI parts and using C code with C2H:
http://www.altera.com/literature/tt/tt_nios2_c2h_accelerating_tutorial.pdf
http://www.altera.com/literature/tt/c2h_tutorial.zip
it's a pretty standard algorithm so you'll probably find many implementations of it in hardware as well as altera providing it as a megafunction that you parametrize as well.