the board "theonewithnoname" linked, does this for you.
otherwise, you are going to have to run the video output of the xbox into some sort of converter to display on an arcade monitor...
NTSC composite to RGB or Svideo to RGB (whichever you have) but...neither of which look great.
unless you mod the xbox itself to output RGB, you aren't going to get a real great picture out of it.
alternatively, you decase a TV with the appropriate connection for your xbox to fit inside a cabinet and display it that way.