How does a member go about wanting to start a private forum where they are the group leader? How do they request it, and or now that this is possible? Are the hoops you have to jump through really as involved and detailed to create?
Create a group, then you can create a forum (in ACP) and assign viewing permissions for only that group and site staff. Make someone owner of the group and then they can be in charge of accepting applications into that group.
Done.
If you wanted you could set up a process where you have a page where people request to have a group forum made for them; they fill in some stuff and hit submit and the admin get a request which they can approve or deny. That would be a custom page , or you can just make a requests forum and subscribe to it.