I'm trying to figure out the best way to show a projector showing clips like key events over a lifetime. I'm thinking a montage with some dialogue, but I'm not certain that's the correct way.
Avoid thinking about challenges with storytelling as having correct or incorrect solutions
Rather, think about solutions as more or less effective given the story being told. Some approaches that work terrifically in one story might not work well for others. The medium is also important, but that is a whole other topic. Briefly stated, stuff that works great for video and film may not work well when writing.
That said, if this "projector showing clips like key events over a lifetime," is a short scene or even chapter, then a equal mix of POV character reaction, narrative text, and dialogue could be an effective approach to creating an immersive moment. Mostly, I imagine focusing on the POV character's thoughts and observations to set the stakes as well as the character's hopes and fears about what they are about to be involved in.
If, on the other hand, this is more of a Clarence the Angel getting briefed on George Bailey in the first hour of "It's a wonderful life" kind of thing, then it seems using the content on the screen as a framing device to segue to a flashback would be an effective solution. In the flashbacks, you get the bonus of being able to share the scene from a different character than the POV character watching the presentation. And, that could get really interesting.
User52445 is correct, for the most part...
This is up to you, as the author.
There is no correct way, but it would be criminal if I didn't at least offer a suggestion: describe every slide in detail. It doesn't have to be a whole lot, just enough for your readers to understand. Try a test audience! That's always a good way to see how well you've done something.