Go to Special:UserRights, type in the name of the user you want to promote and then click the "load user groups" button. Once the user groups load up, you can select any of the user groups under the "Groups you can change" column, and then when you're done scroll to the bottom and click the "Save user groups button".
If you are a bureaucrat on the wiki, be sure to not give users bureaucrat status unless you absolutely trust them. Once someone has bureaucrat status, only Fandom can take it away. Meanwhile, as a bureaucrat, they are immune to blocks and can promote any user they want to; even their own alts.
Did you got to Special:UserRights here on Community Central, or on the wiki where you're the admin? Because you can only promote people specifically on the wiki where you have admin rights. My apologies, I wasn't very clear in the first reply.