Thanks for that data sheet. Unfortunately is is not very good. While all the actual words are in English there is little sense in it.
How did you decide the baud rate was 9600? While it mentions the baud rate in the fault finding section:-
baud rate is not set in accordance
Their is no other mention of what speed it should be. Unless you know this then you can not hope to get it to work.
What have you done with the trigger input? It says in another of those poor phrasings :-
When reader in tigger work way, if make down-lead connect with low level trigger, then reader begins to read card numbers till high level is recovered.
This seems to suggest that the trigger pin should be held low when it will keep on repeating a read tag until the trigger pin is set high. I notice in your code you do nothing about the trigger pin. Before you connect it to your Arduino you have to check what voltage is on that pin. If it is 5V or less then you can connect it directly to an Arduino pin, if not then you need to put the Arduino pin through a transistor first.
I did follow that product tutorial on wiki to test the RS232 shield but what I found is the tutorial seems like only using the Arduino instead of the shield(maybe I'm misunderstood the tutorial).
Yes I think you did misunderstand the tutorial what were you expecting?
That shield uses the hardware serial port. Therefore you can not use the serial monitor on the computer and the RFID reader at the same time.
You have to use software serial to output your feedback to the computer and then you need a USB to TTL serial converter to connect this software serial back to the computer.
Alternatively you can use software serial for the RFID reader and rewire the shield to use the the software serial pins.