I was wondering how do you go about installing G Sport Plegs on my bike. I mean does the nut tighten up against the metal insert or in it or what?

Thanks.

Yup. It's just that simple.
Insert the metal insert into the peg, then put the peg on like you would any other peg.
Note - if you have a 19mm nut, it likely won't fit or at least the socket won't fit in there. The Pleg was designed around a 17mm nut max.
-Bill