How can we give special access (like an administrator) to somebody else?

Please ensure that the person is added to your organization. This can be either as an employee or a contractor.
Go to that person's profile from the People page. Scroll to the User Role / Privileges section, and click on Assign New Privileges.
From the drop-down, select the new user role that you would like to assign to that person. There are several pre-defined roles for you to select from.

If required, you can also tweak the permissions that each user role has, by going to Settings > User Roles > Create/Edit roles.

To see a list of people who have special user roles assigned to them, please check Settings > Collaborators.

To create custom user roles specific to your organisation refer this article.