The more common "angular way" of hiding/showing DOM elements is to use the ngHide and/or ngShow directives -- "declare" them in your HTML (hence this statement on the Overview page:
Angular is built around the belief that declarative code is better
than imperative when it comes to building UIs and wiring software components together
Similarly, to add/remove CSS classes, use the ngClass directive in a declarative manner. Changes to your models (i.e., $scope properties) should drive the hiding/showing and the addition/removal of CSS classes.
If you need something more complicated, put DOM manipulation into custom directives, normally in the link function.
In a jQuery world, we think about events triggering DOM manipulation code (e.g., call remove() on some element). In an AngularJS world, we want to think about events triggering model changes, which then trigger UI changes automatically, based on our declarative HTML (e.g., an ng-click sets a $scope property which is tied to an ng-show on an element). I'm still adjusting my thinking.
For most AngularJS applications, you won't need to use $document.