// load the update-descriptor
var loader:URLLoader = new URLLoader;
loader.addEventListener(Event.COMPLETE, onLoadComplete);
loader.load(new URLRequest('http://mariusht.com/files/products/notelist/update.xml'));

2. Check and see if a user has the latest version of an AIR app installed.

private function onLoadComplete(event:Event):void
{
    // ignore xml declaration
    var str:String = URLLoader(event.target).data as String;
    var index:int = str.indexOf('<update');
    str = str.substr(index, str.length);

    // convert String to XML
    var remoteAppXML:XML = XML(str);
    var ns:Namespace = remoteAppXML.namespace();

    // get new version number
    var version:String = remoteAppXML.ns::version;

    // get current version number
    var appXML:XML = NativeApplication.nativeApplication.applicationDescriptor;
    var ns:Namespace = appXML.namespace();
    currentVersion = appXML.ns::version;

    if(currentVersion != version)
    {
        // download AIR file
    }
}

3. Download and save the AIR file. Don’t forget to call Updater.update() function.

public class UpdateAppCommand extends SimpleCommand implements ICommand
{
    override public function execute(note:INotification):void
    {
        // download updated .air file
        urlStream = new URLStream();
        fileData = new ByteArray();
        urlStream.addEventListener(Event.COMPLETE, loaded);
        urlStream.load(
            new URLRequest('http://mariusht.com/files/products/notelist/NoteList.air'));
    } 

    private function loaded(event:Event):void
    {
        urlStream.readBytes(fileData, 0, urlStream.bytesAvailable);
        writeAirFile();
    } 

    private function writeAirFile():void
    {
        var file:File = File.applicationStorageDirectory.resolvePath('NoteList.air');
        var fileStream:FileStream = new FileStream;
        fileStream.open(file, FileMode.WRITE);
        fileStream.writeBytes(fileData, 0, fileData.length);
        fileStream.close();

        var versionProxy:VersionProxy =
            facade.retrieveProxy(VersionProxy.NAME) as VersionProxy;
        var updater:Updater = new Updater;
        updater.update(file, versionProxy.version);
    } 

    private var urlStream:URLStream;
    private var fileData:ByteArray;

Related Links:
Updating AIR applications (Adobe AIR 1.5 LiveDocs)