Today the MFRC522 RFID reader I ordered some weeks ago arrived. Using it with an Arduino proved to be pretty easy after I found this blog post.
The crucial part from this blog post was the pin map … every other blog post or forum thread was about software, nobody noted how you have to wire it up. The Arduino code provided on this post is a little confusing … I have the impression it is a chinese translation of a code snippet I found on another site before, which only merged the code from module and sketch from this GitHub repository into one sketch file, making it extremely difficult to read. The code from Miguel Balboa on the other hand, while much more tidy is lacking information on how to use it.
So, this is how I wired the RFID reader to the Arduino, using the notations on the PCB:
This way I was able to use Balboas sketch and module without modifications.
In the comments some people asked how they can make the RFID module work with other Arduino variants. It is really difficult to help with hardware I do not possess myself, so you can only hope that somebody else reads your comment and can help you. You will get much better help when you ask on a dedicated community site, I can highly recommend the Electrical Engineering Stack Exchange site.