I have an older version of this shield working perfectly in my arduino duemilanove. You could use it with your arduino mega, but you need to include some other libraries to connect it in the same position that on the Uno or Duemilanove boards. However, if i am right, in the lower part of the SD shield you have a 2-colums 3 pins conector. Is it right? This id for the ICSP connection. You must connect them directly to the ICSP pins located in the middle of the arduino Mega board. Just only take care, because you MUST also modify the selector located on the higher part of the Sd shield. Now it is connected to 5V and 3.3V. Remove it and connect again to the 3.3 and GND (just the third one previously free). That is all that you need related to hardware.
About software, you have available different libraries: SD, SDFat, Filelogger,... and so on.
Please, check the links contained in the webpaged you linked in you post, because there you have everything that i explained to you, including schemes and plots of how to wire it to the boards, as well as tutorials.
I hope it could helps you.
Thanks for your answer MadePablo. I think I forgot to remove the selector, because that's the only thing I done wrong. For the moment, my method is working well for what I want to do, but I prefer yours, it is more "clean". I will try this later because now I would like to try other thing with the SD Card.
Thanks a lot for your precious help.