Making a private forum is easy, setting up the access gets a little difficult...
Make the forum and when you're setting it up, theres an option to make it open to the public, and it defaults to only admins and supermods getting in. You can then modify that thru the forum permissions. To let one person in, you have to modify that persons personal access... which is a pain in the ass, so I make a custom usergroup, but seeing as the person can only be one, you can only give him access to one.
For the link thing, Just put a regular old html link where you want it... Then open up the private forum copy the address out of the address bar and paste it into the link on the html page.
that help?