How do I add embedded YouTube videos in a field?
Just use the Video Filter module, here is a quote from its project page:

This is a highly flexible and easily extendable filter module to embed any type of video in your site using a simple token. Other modules can add video sites/formats (called codecs) using an easy plugin architecture.
With WYSIWYG installed, you can use the Video Filter button to easily add videos in a rich text editor.