I recently did it with my GTV. I don't recall the step by step, but it's not a straight forward parts swap so be sure to save all the parts from the old handle before tossing it.
The reason the swap isn't a straight "replace the old core with the new" is that in order to keep costs down on the newer handles, they made the core, and the internal part that attaches to it with a roll pin, interchangeable for both the drivers side and passenger side, whereas on the original handles (at least on my '73), the core and the internal parts were "left handed" for one side and "right handed" for the other.
So in order for the old cores to work in the new handles in the same fashion as the original handle, I had to scavange the part that attaches to the old core from the old handle, so the core would turn the same way. It won't with the "wrong handed" newer part. It took a little figuring out, but if you're mechanically inclined, you'll figure it out once you get it apart.
Also, for whatever reason, the new handles did not seat in the door panel opening in the same way. Don't get me wrong, it fit, but it wasn't an exact fit like the old ones. and I had some small gaps between the door skin and the flange on the handle. So even if it wasn't original to the car, I added the rubber gasket, that you can buy from IAP or Centerline, that fits between the door skin and the handle. That took some fiddling too, and there's a thread on the BB about that where I posted some pictures of what I did... and in those pictures, you should be able to see the part I was referring to earlier that's attahced to the end of the cylinder.
http://www.alfabb.com/bb/forums/gt-1965-1974/170924-gtv-outer-door-handles.html