When you first make a new profile, you will be prompted by the "Quick Edit" modal to add more information about the individual, such as date of birth, phone number, email, address, etc. You can add info here or exit the modal and add these items later.
Make sure you are in the "Contact info" section of the profile.
Scroll down until you see the "Contact" section.
Locate and click the + icon at the top right corner of this section
Select "add phone" from the dropdown.
This will open up the add new phone modal to fill out.
NOTE: It's a good habit to mark at least one phone number as "preferred."