The Flash Player renders the scene in regular intervals based on a framerate. You can be notified about the beginning of the cycle with the Event.ENTER_FRAME which is dispatched by every DisplayObject... which is pretty much anything that you can display, including your main class that Flash Develop sets up for you.
To animate an object over time, register an event handler for the ENTER_FRAME event and modify anything you need there.
// in some function
addEventListener ( Event.ENTER_FRAME, enterFrameHandler );
protected function enterFrameHandler ( e : Event ) : void
something.x += 5;