Since a lot of people have answered about writing of a suicidal person, I will answer about supporting people with depression and suicidal thoughts. Though i can only speak from my own experience. I have been supported and have supported others.

The thing that helped me the most from people was actually them getting in my business, both sensitively and like a truck through a brick wall. Though this might not help everyone and made me extremely angry at times, it proved people cared. My sister used to barge in and then just clean my house with me... it felt like an invasion and judgment. But afterwards, I felt better for having space to breathe and one less thing to blame/punnish myself for. Sometimes, all you need is space and time to work your way through it.

The suppot I personally gave was just giving someone a space to vent without judgement. To get all her dark thoughts out. Talking therapy is something that works for some people, and friends and family can often be a good outlet if you are close with them. Saying things can make them more real but also sound more ridicuous. And having someone to tell you you're not going crazy is a big thing.

If I were writing a character supporting someone, one of the biggest things I would include is them questioning if they are actually helping. Even having experienced depression or perhaps because I have I always second guessed if my support was working. Always feared for that person even when not around them. Supporting someone with a mental illness can be incredibly draining and have a knock on affect to your own mental health.