So, actually the complete guide to support multiple resolutions is stated clearly here, which includes the 3 strategies:
a) Stretching the stage
c) Smart Object Placement
In this post, particularly, I will demo a quick and an easy approach - Stretching the stage. Just in case you are still getting stuck with the guides, here's a simple working solution for your reference (which i actually use it in all of my games :))
public class myGame extends Sprite
private var mStarling:Starling;
public function myGame()
// support autoOrients
stage.align = StageAlign.TOP_LEFT;
stage.scaleMode = StageScaleMode.NO_SCALE;
var screenWidth:int = stage.fullScreenWidth;
var screenHeight:int = stage.fullScreenHeight;
var viewPort:Rectangle = new Rectangle(0, 0, screenWidth, screenHeight)
mStarling = new Starling(Game, stage, viewPort);
mStarling.stage.stageWidth = 640;
mStarling.stage.stageHeight = 960;
// set anti-aliasing (higher the better quality but slower performance)
mStarling.antiAliasing = 1;
// start it!
What is actually done is that, in the codes, i have defined my default device to be a screen with the width = 640px and the height = 960px (ratio w:h = 2:3). With this, all my game elements (buttons, background images, etc) would be designed based on this resolution. Then, if the game is loaded into a device with a different screen size (and pixel density), the Starling would help me re-size accordingly. It could be a compromise, but it will effectively save you a lot of time.
Isn't that easy and convenient compared to that in the Java Eclipse?