I think the most important way in which others can help self-harmers is by LISTENING and NOT judging them. It is often very hard to even try and contemplate why a person would ever want to deliberately injure themselves and if it is someone you care about it can be very distressing and frustrating for all involved and it is ok to seek help from others yourself in helping the self-harmer.
If someone has told you that they self-harm then it is because they trust you! This is often the biggest step for them because self-harm is not something they are proud of and often they go to great lengths to hide it. You have taken the time by coming here to try and understand and learn more which is a very good thing. It shows that you care and that is above all a supportive thing to be doing.
It is important not to be sickened by a person who self-harm's purely because you don't understand, they are still the same person you knew before you found out they harmed themselves. They need you to loving them in the same way as before. If not more.
Self-harmers are often scared that when people find out they will 'disown' them and threaten to walk away if they don't stop immediately; this is an unrealistic burden on a person as self-harm is in many ways an addiction, it is doubtful that they want to harm themselves, they feel they need to for whatever reason and would probably have preferred to have stopped rather than admit the problem to anyone. *Threatening the self-harmer will do nothing other than isolate them further and probably stop them from confiding in you again so however much you want to scare the person into quitting you probably won't.*
Self-harm is a private act and making someone who doesn't want to talk about it discuss it with you you are intruding in their own personal space. Make it clear that you are always willing to listen and will be there for them without judging but please don't intrude because you may cause more pain to them in the long run!
It may be tempting to rush the person who harms themselves straight off to the doctor/psychiatrist/counsellor/local psychiatric ward but that is rarely the answer. People seem to believe that the medical profession can instantly cure anything but this is not the case with issues such as these. Psychiatry and drugs have had little success in dealing with self-harm so as much as you may want to get that kind of help for your friend or relative and as much as you may think it's 'for their own good' please reconsider and instead ask them what THEY would like you to do for themselves. When they are ready to get help from other. Don't worry! They WILL!!! All you can really do is sit back and be the BESTEST friend they have ever had. BY LISTENING!!!