question, sorry if this is a repeat...

how exactly are the side windshield moldings supposed to be held on to the car?

I had my windshield replaced, they also replaced the moldings. One flew off about two weeks later, so I bought another replacement, but haven't put it on yet.

 

They are just pressed on. When I bought my car, one of them was missing and the previous owner said it came off in a car wash, it was still in the trunk. I simply pressed it back on, and it has stayed on for the last 2 years without any issues.

 

I tapped them in with a rubber mallet. Start at one end and tap them into place along the entire length until they are flat and seal up against the windshield.