How to capture wireless signal?

Try looking for a RF Transciever module on the internet. Such a module should be a simple board that has an antenna, tuner, amp, and a digital interface. It will likely have about 4 digital I/O pins that can be connected on the FPGA board's GPIO.

You can build an embedded SOPC with a NIOS CPU that controls the transciever, and that sends/recieves the information on the channel you want to tune into.

As an experiment you could use two such transciever modules; one of the modules could be connected to a breadboard with a microcontroller and LED, and the other module could be connected to the FPGA. Then have the FPGA send commands over the air to the other module, which the microcontroller can then decode and then light the led.

A wireless light switch... A good way to experiment with FPGA wireless.