How is the collapse of the wave function explained through electron atom scattering?

I have learned from this answer/comments that people have put much effort into understanding how scattering of electrons on atoms could explain where, for example on a screen behind a double-slit diffraction experiment, light flashes appear as a result of what is often called "wave function collapse".

Since wave function collapse (from an extended to a localized wave function) is commonly considered an indeterministic event, I would like to understand, what the treatment of electron-atom scattering could add to the picture of where or why an electron flashes on the screen.

Is there a way to explain the essential insights of these analyses in rather simple words?