First step is to apply butyl tape to the window perimeter where the frame will meet the plywood panel.

We made a template from cardboard using the trim ring as a guide. We positioned the window on center horizontally, and 1" down from the drip rail.

Then we drilled 3 holes using a non-symmetrical pattern so we couldn't get it wrong on the inside (next photo).

The template is then matched up to the holes on the inside, using drill bits to hold it in place. We traced the template onto the wall.

For the first cut I used a shorter, metal-cutting blade in the jigsaw. (The larger teeth of a wood blade seem to get bound up in the fibers of the cotton insulation. The finer teeth of the metal-cutting blade had less of a problem.)

The 1/4" birch scrap promptly fell into the gap behind the paneling :-(. We cut away the cotton and foam insulation with a utility knife, leaving the 3/4" exterior plywood exposed.

Ouch, the foot of the jigsaw mars the wall a little. I think it can be repaired with some light sanding and touched-up with shellac.

The final cut was made from the outside, using the same metal-cutting blade.

After some minor clean-up with a sander, we insert the trim ring from the inside and the window from the outside. We used 3/8" #6 (x12) metal screws to attach the trim ring to the groove in the window frame.

The aft window (on your right) was moved forward a few inches to accommodate the shower wall.