Is there a way to dynamically add input fields to a form?

I have a Contact table with a Phone subtable. The Contact can have more than one phone number. I want to design the Contact edit page’s phone field similar to the phones field(s) shown in this video.

1. Has anyone does something similar where you can click a button and have it add additional fields?
2. How would you submit each row as a record within the larger form that will be submitted?