Well first of all It's very kind of you to do this, really. Glad you can help others this way.
Don't know which hotline you are at or if you have started, most have restrictions, guides and scripts. Maybe they won't let you say what you'd wish. Not sure, but have that in mind.
But if anything yeah, empathy is important. If you can relate to them, let them know that they are heard and that others have also gone through that, you yourself if that's allowed, just that alone can help a lot when you feel very miniscule and lonely.
Listening in general too. Once I yapped for like 10 mins before realising they had hung up on me, and I was really enjoying it, 10/10 service, thought they were really good listeners lol.
Maybe intercede and slip comments if you hear any particular problem they express that deals with the psychological, and thus can have some workarounds. If there is some technique they might not be aware of, truths that are easier to spot from the outside and need to be heard then, like "No you are not a worse person or weaker for being depressed while having it better than other people, there are no ideal circumstances" or similar. Those are the ones that can be more easily tackled or at least there some room for words with actual impact and advice there.
For most other external problems that drive people to suicide... yeah there's very little you can do from over the phone. But they are calling for help. And so I think it's best to realise that sometimes whichever comfort you can bring them in that state has to be good enough. Can't solve the issue, maybe acknowledge that fact, but you can relate, feel them, hear them out, say what advice you can trying for it not to be pandering. Shit is hard and often unsolvable and complex, and I'd much rather someone acknowledge that, do what they can, be there to just listen than getting the sadly common dismissive "it's gonna be okay" catchphrases... which yeah I get where they come from, but you are instantly reminded you are talking to an instruction manual on how to defuse a person with magic words.
So I also understand callers, and tho there's variety, with some I've heard the most broken tired voices from their end of the line. Specially if you call at night. Take care of yourself and take it easy while doing this, again it's incredibly kind and goodhearted you do, but you know how it can drain.
hugs <3