The basic idea behind a support group is just to get people with the same issue together and talk about it so that people can learn from the experience of each other.  The most important aspect is probably secrecy.  People need to be able to trust each other to open up, which is why what is said in the group stays in the group for most support groups.

Beyond that, it really depends on the overall goal and what the people you have are.  A key skill for someone leading such a group is to be able to get people to open up.  If people don't open up about what they are going through, it's of very limited value.  Beyond that, if the group is being directed in a particular way, then you would need more general psychology background to help steer the conversations in much the same way that a guided one on one session works, but with multiple people participating which can change the dynamic quite a bit.

Ultimately, it is mostly about providing support though by showing people that they aren't alone and that they can help each other, so it's less about the leading and more about the group.

Alcoholics Anonymous is probably one of the most successful support groups out there and they have a lot of good information publicly available about how to start an AA group.  [This][1] is a document that they have about starting an AA group.


  [1]: http://www.aa.org/assets/en_US/general-service-representative-gsr/p-16-the-aa-group