I've had no such training per se (that's a thing?), but I've been suicidal myself, so perhaps my perspective can be of help regardless.
One thing that's important to know: if someone tells you they're gonna kill themselves? Boy is that a cry for help, because just being suicidal doesn't mean you're actually gonna commit the act, much less tell anyone about it. There's a huge difference between being suicidal and really going the extra mile to try and commit suicide. Basically, there's a spectrum of suicidal ideation you have to be aware of.
So, if someone were to outright tell you they're thinking about suicide? Be there. Talk to them. Ask them what makes them think about killing themselves. What makes them hopeless? Listen. Really listen, and don't talk over them. Understand that their feelings are valid, that this is their reality. Try nudging them enough in a direction where you can ask what could ease their hopelessness. What exact measures could you as a friend take to make their situation better? What do they need? Do they feel like there's nothing in their future that's worth living for? Can you help them find that "something"? Can you help them find something worth looking forward to, even if it's just a concert of a rad band? A new book of their favorite series? A TV series they've been itching to watch for years? Keep them company. Really give them a sense of not being alone in the world.
The most important thing, from my perspective (so what helped me), was just one simple feeling: acceptance. Accept that this is how they feel. Don't panic. Don't heave your own feelings on their shoulders or they will just feel like a burden to everyone around them even more. Make sure they know that they are NOT a burden. That they enrich your life. That you are dedicated to enriching theirs.
Then comes the therapy (if affordable). They have to be open to get help, after all. If all you feel is hopelessness, that there's nothing that could help you—why would you even think that therapy could change that? You need to have a safety net. And you need to know that there are people to fall back on when therapy is just getting too much (because boy is that hard work).
Well, tldr; be there.
And be aware that suicidal ideation often doesn't just go away. I'm still living with it, only it's just kinda... floating around me lol. Some people never get rid of that feeling completely, and that's okay. We learn to manage the worst intrusive thoughts, wave them off. But the way is long and you need to be prepared to work hard if you really want to help—because depressive people can't just "reach out" like so many people urge us when another celeb has committed suicide.
I hope you never need to apply all these thoughts, of course. But keep your friends in mind, as depression is on the rise while capitalism is growing worse and worse;;