As more and more people use the internet, long-distance cries for help are getting more and more common. If you were in the same room, it would be best to help that person find someone who is trained in this sort of situation. Around here, I'd contact a counsellor or take a suicidal person to the nearest hospital. But you can't do that over the internet and we don't know who would be best to help someone who lives in a different culture. So I'd say the best thing to do is what the Community Team does when these situations come up on the network. We send a personal email like this:
[Introduce yourself if appropriate.]
I'm concerned about you. It sounds like you're [explain how you heard the other person is feeling down or in a tough situation].
If so, I recommend calling the National Suicide Prevention Line (1-800-273-8255) or use their online chat [http://chat.suicidepreventionlifeline.org/GetHelp/LifelineChat.aspx]. The people there are on call around the clock to talk to people struggling with the same kind of issues you are. Despite the "National" in their name they're happy to talk to people outside of the US.
Please respond to tell me that you'll either contact one of the resources above, or just go to your local emergency medical center right away. The most important issue here for us is making sure you are okay.
Generally I'd want to use my first name to try to make a human connection. I'm not trained to give advice in this situation, so my primary goal is to get them in touch with someone who can help. Every now and then I get a response, which is wonderful. More often I never hear from the person again. It's unsettling to think about, but it's not my responsibility (or even possible) to help everyone who needs it.
If you are using a medium other than email, I encourage you to find a private space to communicate. On Stack Exchange, we delete posts and comments that indicate a desire toward suicide or self-harm. It just draws unnecessary attention and poses a copycat risk. Since email is suitably private (normally) and most everyone has access, it's usually a good way to go.