Need help with communicating with card reader!
I'm not sure what you are expecting, but you should realize that you need quite a lot of software to read RF cards with these chips. I've done it and it took several days of coding. Luckily, as pointed out by @MarkU, there's a lot of example code floating around in the web. There's these nxp examples (http://nxp.com/documents/software/200312.zip) (which I looked at but ended up writing the code from scratch). And there's now an Arduino library, which could be helpful also. 

In case it's your impression, it's not just a matter of pulling low a chip select and clocking in the data from the card. First you need to take control of the MFRC522 chip so that you know how to send data packets to the air with the correct baudrate, format and RF protocol for the RF card you're reading. I ended up winding a 5 centimeter coil with a few loops and connected it to an oscilloscope probe to be able to measure the RF signal, and eventually snoop the traffic between the reader and the card, just to see if the card seemed to be doing anything at all. (For those interested, I also rectified it with a diode and filtered with a small capacitor to get a functional trigger signal for the scope and it was really helpful).

Once you have the MFRC522 under control, you must support the higher-level RF protocol to select the RFID card and read data from it. That's not a trivial task, either. But of course, the now existing example codes help.

You didn't say that you had a microcontroller in your system or that you're using a soft CPU core in your FPGA. I'm asking this, because writing the control code in VHDL would be very very tricky. I'm not saying that it's impossible, but you should have a working software implementation first.