You'd do it so that the "other player" that you can see is actually a completely new object, but is told to move, when the person controlling the "other player" presses buttons etc. Then you'd make it so that if the user of the "other Player" presses the button to change weapons, that the character that you can see changes his weapon.
You must remember, these games will not be the same exe (from two different camera views) it will be an entirely different exe from possibly across the globe, so you need to think about data transmittion sizes etc, therefore instead of sending the data of say the entire mesh state of "the other player" you just send the buttons pressed by the other user and change the mesh of the "other player" accordingly.
Hope I Explained that ok...

Team EOD :: Programmer/Logical Engineer/All-Round Nice Guy