This sample project achieves exactly the same functionality and look as the edit UI in the stock Android contact app (or "People"), where you can remove a row field view by pressing the "x" icon on the right, and add a row field view by pressing the "Add new" button at the bottom.
The example also handles some visibility logic for better UX as in the stock app: If a row becomes empty, "add new" and "x" will disappear.
Here is a demo video in action: http://www.youtube.com/watch?v=4HeqyG6FDhQ.
The state of the views is not saved for rotation. You'll need to work with onSaveInstanceState and onRestoreInstanceState. I left some notes in the code you can start with.
My original stackoverflow answer with some details: link
TextWatcher, setVisibility, inflate, addView, removeView, animateLayoutChanges