Before I begin you may want to take a look at the Angular-UI project on GitHub and see if the that covers any of the jQuery UI or even Bootstrap functions you're looking for before you go ahead and create your own.
Lets take jQuery UI's drag and drop interactions also known as "draggable" and "droppable" and ready them for use with AngularJS.
First, lets decide that we just want to be able to add our directive as an attribute to an DOM element we already have on a page which would then enable that element to be dragged around. So here's how we want that to look:
<div id="myElement" class="myClass myOtherClass" angled-draggable>[...Some Content...]</div>