I reviewed the stuff I'd learned back in high school ("Listen." "Be supportive." "Don't argue." "Etc etc etc.") I have trouble believing that this would work outside of movieland, especially on strangers. More so, in person I'm an awkward, fidgeting introvert---the impact of everything I say is thus diminished, and I sound very insincere or nosy, like I'm following a bad movie script, when I say anything like, "You are not alone in this. I’m here for you." or "How can I best support you right now?" I doubt that this would sound any better in writing.

It might seem to you that this isn't the sort of thing that would work in real life, but in general, yes it does.

If you're worried about sounding insincere, try and think of something genuine and non-trite that you can say. For instance, many suicidal people don't believe that anyone would care or be meaningfully affected by their deaths; try and think of a sincere way that you could tell them that you do care whether they live or die.

Any specific words you might have been taught are unimportant, they're really just a guideline to the sort of structure you ought to assume.