To add an administrator to your Facebook business page you, first of all, have to be an admin yourself!
If you are, simply follow these steps:
1. Click Settings located in the left-hand menu of your Facebook business page.
2. Choose Page Roles from the menu of options located on the left-hand side of your screen.
3. Enter the email address connected to your new admin's Facebook profile and choose which role you would like to assign to them from the dropdown. There are several roles to choose from: Admin, Editor, Moderator, Advertiser, and Analyst.
To see detailed information on what each role can do, please select the role from the dropdown and note the description beneath the role title.
4. Once you have selected the role click Add and you are done!
For more information on Roles within a Facebook Business Page please use this Facebook Help article.