I'll give my advice from a suicidal person's perspective. (I don't know much about self-harm, but I guess there's a lot of overlap.)

TL;DR: The Joiner model of suicide has three necessary and sufficient conditions for making suicide attempts:

1. burdensomeness, e.g. "people would be better off without me",
2. alienation, e.g. "nobody would even care if I died", and
3. desensitization, e.g. they've suffered for an extended period of time; they now prefer to cause their own death over suffering.

Stack Exchange has very little impact on any of these, but if you treat them like a normal human being, and simply listen to them, you can slightly reduce (1) and (2). And please, do NOT copy/paste canned comments about suicide hotlines, you'll make (1) and (2) slightly worse.

Regardless of anything else: (a) you are not responsible for someone else's suicide, and (b) you're not capable of long-term preventing someone suiciding. So don't be afraid to be yourself.

Some basics....

The Joiner model of suicide has three necessary and sufficient conditions for suicide attempts:

1. Perceived burdensomeness. Examples:

   I am thus a burden to her and think that it would be best to relieve her of my presence.
   _Suicide.org

   I just feel like i’m a burden to everyone around me – sometimes i think if i wasn’t here anymore, it would make everyones lives that bit easier.
   _{Suicide Project}

2. Low belonging/Social alienation. Examples:

   I always used to wish for friends and have people to interact with, but now I feel like loneliness is better for me. I'll have fewer people to disappoint when I finally ctb.
   _{Sanctioned Suicide; (note: ctb = "catch the bus", slang for suicide)}

   Nobody really cares about me and I dont think they would give a flying fuck if I'd die.
   _{Sanctioned Suicide}

3. Acquired ability to enact lethal self-injury. This is succinctly described as desensitization to the idea of killing oneself.

   The few who can have developed a fearlessness of pain, injury, and death, which, according to the theory, they acquire through a process of repeatedly experiencing painful and otherwise provocative events.
   _{The Interpersonal-Psychological Theory of Suicidal Behavior: Current Empirical Status (emphasis mine)}

So no matter what you say or do, you're incapable of causing or preventing suicide on Stack Exchange (barring e.g. extreme cyberbullying): you're not going to affect these things in any major way. So relax, and be yourself: act as you normally do. Be honest. Be a human being. If you act abnormally, you're going to exacerbate the first two feelings.

I know no one wants to be the one that "pushes someone over the edge", but it's not your fault if that happens. These three conditions did not arise because of what any single person has said on Stack Exchange.

Asking “why,” she explains, assumes that there was a single cause, when in reality, people die by suicide for complicated reasons.
_{WebMD (emphasis mine)}

The advice given over and over is to simply listen without judgement. It's the same advice again and again: listen, listen, listen, listen, listen, listen.

The most important thing is to listen to what they say to let them know you care. ... It is also important to avoid making judgements about how they are thinking and behaving.
_{Suicide, HSE.ie}

What not to do...

TL;DR: Do not copy/paste. Do not suggest a suicide hotline. Don't lie. Don't treat them like a baby. Don't try a quick-fix.

Suicidal people are encouraged to be open, and talk about their suicidality---it helps. But the instant you do, people begin acting very weird. Anyway, here's my tips:

• Do not copy/paste from a script. It feels incredibly cold to get a copy/paste message when you're contemplating suicide. I realize there's a +95-score answer that basically says "copy/paste this", but I'm going to flatly contradict this: do not copy/paste!

  1. You can assume that 100 people have previously copy/pasted an equivalent "answering machine" message. You're sending them spam, not help.

  2. Do you remember how people felt about this canned response? Now imagine receiving a canned response over and over again, every time you try to open up about suicide. On top of the coldness, it inhibits suicidal people from reaching out; they'll just anticipate getting the same copy/paste response.

  3. When I receive canned responses again and again, I go from "maybe there's something I haven't thought of" to "I guess there's nothing left to discuss", which is when suicide becomes actionable.

• Do NOT suggest calling suicide hotlines. This is not about helping others; this is an almost-zero-effort way of making yourself feel good. There's multiple points here:

  1. We know!: Suicidal people go to Google and search for how to kill myself, and they will have to wade through hundreds of these numbers and websites to actually reach sites with usable information. Rest assured, suicidal people are not ignorant of these phone numbers.

  2. Unvetted: People are less selective with suicide hotline numbers than they are for pizza delivery. It's insulting when people copy/paste the first number they Googled; you might as well write let me Google that for you.

  3. They can totally mess up your life: involuntary commitment, having the cops called on you, child custody, permanent medical records, losing your job/career, getting hung up on, massive medical bills, hurting your friends/family, suicide watch lists. And in some countries, suicide is a crime.

     There's the pages and pages of horror stories of people who call these numbers on Reddit. E.g.:

     I've called before, I'm going to be honest, and I was treated like a child. They just try to weed out your information on the sly to "save" you and treat the call like an improv class. "Yes, I understand", "Yes, that must be hard". There is no real help provided and they don't actually sit and talk to you when you need someone. ...
     _{Reddit r/UnpopularOpinion}

     See also this November 2019 survey on the pro-choice site Sanctioned Suicide:

     If you have ever called a suicide hotline what was the result?

     • 56.7% negative;
     • 37.5% neutral;
     • 5.8% positive.

  4. Why don't you call them?: If you see someone talking about suicide online and you genuinely (but likely mistakenly) believe a suicide hotline would help: you call it first! You can ask for advice for how to help this suicidal person, and you can vet the hotline too.

     And if you find yourself thinking ...but that phone call could totally mess up my life, you're probably right. And hopefully you now understand why you shouldn't suggest it to others.

• Don't lie. Why do people think it's okay to lie to suicidal people?

  1. Don't say "it gets better". People's deceased loved ones stay deceased; memories of childhood abuse do not "get better"; amputated limbs don't grow back; memories of being arrested don't just vanish; you will not be wealthy throughout your life; your ex-partner will remain your ex-partner; LGBTQ+ people will continue being mistreated simply for existing; you will not forget those careless words you said that hurt someone; you will not get younger; your incurable illness will remain incurable; you are not rich enough for a lawsuit and have to accept injustice; you will continue to be discriminated against for your religion or lack thereof; and you will eventually die regardless of how much you suffer. (And in about 100 years time, whether you kill yourself or not, you will be totally forgotten.)

     Please, never make promises to our vulnerable OPs that you personally can't keep. This means not saying "it gets better" or guaranteeing any outcomes!
     _{Reddit r/SuicideWatch}

  • Of (a) "it gets better", (b) "it stays much the same", or (c) "it gets even worse", the least likely to occur is (a). Since these things tend to accumulate over time, (c) is the most likely. Also, let's think about the logic here...

    1. it gets better => don't kill yourself
    2. it doesn't get better => ???
  2. People who lie lead to mistrust of the people who don't lie. They'll think people say certain things because it's socially required, not because they actually mean it.

• Do not infantilize them. People start treating you like a baby, not as an adult human who is capable of independent thought and decision making.

  Studies have shown that an individual, when infantilized, is overwhelmingly likely to feel disrespected.
  _{Infantilization}

• Do not attempt a quick fix. It's patronizing having people who are ignorant of 99%+ of your life spruiking an off-the-top-of-their-head solution to all your problems, as if you've been incapable of thinking of 5-minute solution all this time. The suicidal person understands their own situation better than you do. It's even worse when they get angry at you for not listening to their solution.

  Don’t try to fix their problems. Listen with empathy and without judgement. _{Beyond Blue}

• Don't disbelieve them. It's pretty standard to declare suicidal people as "just want attention" or something.

  ...in at least 80 percent of completed suicides, the people provide verbal or behavioral clues that indicate clearly their lethal intentions.
  _{Understanding Suicide - Common Elements}

• Don't say "suicide is selfish", etc. Anything like this just adds more guilt. And often the opposite is true: people kill themselves in the belief that it will give their loved ones a better life.

• Don't bring God into it. Or at least, you should be pretty sure that this topic is welcome before doing so. Sanctioned Suicide's survey lists 78% atheists.

  Religiously unaffiliated subjects had significantly more lifetime suicide attempts...
  _{Religious Affiliation and Suicide Attempt}