This page describes installation with an older mandrel that has been improved in modern rivet nut tools. This page is valuable only for the views of the installed nut, not the mandrel.

Older mandrel and rivnut. Hole is an F drill or .257 diameter.
Older mandrel in rivet tool. Rivnut tools now come with better mandrels threaded at both ends.
Here the rivnut is in place and the tool is set to pull the mandrel down, crushing the serrated rivnut barrel. This takes some muscle to compress the barrel, so squeeze hard but slowly and watch the barrel closely.
You can now see the barrel is bulging slightly. This has caused it to expand and grip the inside of the hole. This is all that is needed. All you need to do now is verify that the nut does not turn .
Now you remove the rivet tool and take out the mandrel.
This is how it will look on the outside of your garage door ready to install the plexiglass windows. Note that the rivnut body will keep the plexiglass from sitting on the metal door so I recommend to put a bead of caulking on the door at least at the top but all around is best.