You can invite a member using the Invite tab on de Invite page.
Inviting a new member implies you are partially responsible for the behavior of this member! Inviting a member that you know is currently banished will possibly get you banished yourself!. Severe misbehavior of any member you invite can have personal consequences.
You can only invite a new member that has completed the first 4 steps (account information and email verification) and is currently waiting for his waiting time to be over. So if you want to invite someone, have them start the registration process first.
Search for the registration process by entering the exact player name in the search field. Select the amount of invitation credits you wish to spend and click 'Invite'.
Keep track of their progress on the History tab of the Invite page.