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From LogicWiki

This page will tell you how to create a new user. You must already have an account and be an administrator in order to do so. Currently, I am making every user and administrator, so this basically means any user can do it.

In order to create a new user for someone. First go to Special:Userlogin. Type in the new username. Don't type in the password, if you leave it blank the system will create a random password for the user. Also type in the user's email address and real name. After this click on the "by email" button next to the "Create new account" button. This will send the user a password.

Now, you need to give the user sufficient permissions. Go to Special:Userrights. Enter the username that you just created and click the button. Go down to the bottom box. You want to add this user to the groups "sysop" and "bureaucrat". "Sysop" gives them the power to delete pages, protect pages, block and unblock users (right), and also to view our hidden namespaces. "Bureaucrat" gives them the power to change other users rights. Don't add them to the "bot" group. This hides their edits from Special:Recentchanges.

That's it.