From The DoY Wiki
How to invite a user
First, they need to have an account. An account on ShoutWiki is global, so if they signed up on another wiki this account can be used here. If they've yet to make one, you can create them one via Special:CreateAccount.
Once they have an account, go to Special:Invite and type in their username. The user will then have access to your wiki, and can view and edit pages.