What do you mean by supposedly? Do you mean people who say it but you don't believe them because they tend to say that kind of thing often?
Quite frankly each time is going to be different, even with the same person. I dealt with this kind of thing a lot (Note: seriously I think people were confusing me with their shrinks) back in highschool, both people who were legitimately suicidal, and people who were "suicidal".
There really isn't any sure fire thing that works every time, but a few things that usually work would be:
1. Get them to laugh or smile, this isn't always easy but it's surprisingly effective.
2. Keep him/her talking, about pretty much anything, it'll keep their mind off of hurting themselves *generally* This also has the added benefit of helping you if you're doing this online, it'll keep you calmer because then you don't get those 10 minute breaks where you get worried sick because you have no idea what they're doing.
3. Physical contact seems to work really well in my experience, this of course varies from just sitting close to actually holding.
A few other random suggestions would be:
Know your subject, This is probably the most obvious thing, but using tough love when sugar coated coddling should be used can break down a good amount of work.
...actually I'm gonna stop it here because most everything else I would say would be extremely obvious and you probably know, and I'm probably starting to sound like a know it all tool.