This is the standard way of adding an admin to your Facebook page. Go to Settings at the top of your page and click on "Settings":
Then select "Page Roles" on the left sidebar:
Once there, add the email address of the person you'd like to made admin - the email address has to be the email address they use on Facebook. You also have to select their level of access your page:
Now our part is done. The person that you just made Admin should get an email from Facebook that looks like this:
This person that just has to hit on "confirm" and voila! Your new admin is added to your page.