Here's how I am planning on doing it and I am wondering if this is correct. I haven't been able to find any how-to-do-it instructions or videos on the Internet.
My plan is to buy a new-construction vinyl window and cut off the nailing fin that is normally used to nail new vinyl windows to the studs. Then frame out the window opening and cut the existing aluminum siding flush with the framed window opening. Then insert the window in the opening from the exterior and secure the window to the studs with nails or screws going through the sides of the window into the sides of the studs. The installation would be similar to installing a prehung door into a similar opening (which I just did in the same wall). The exterior window trim overlap without the nailing fin would cover the aluminum siding, and then I would caulk the aluminum siding where it is under the window trim using clear 100% silicone caulk.
Is this how it is done?