This is the barebones version of what you want to do, the handleEnterFrame function will run once each frame (and for each cloud, but I'm guessing you'll prefer the simpler solution)
package {
import flash.display.Sprite;
import flash.events.Event;
public class Cloud extends Sprite{
public var xSpeed:Number = 1;
public var ySpeed:Number = 1;
public function Cloud() {
addEventListener(Event.ENTER_FRAME, handleEnterFrame);
}
public function handleEnterFrame(e:Event):void {
x += xSpeed;
y += ySpeed;
}
}
}
Set "Export for actionscript" in the Linkage menu of your cloud symbol, and set the class name to "Cloud".
This code should be placed in an external file called "Cloud.as", in the same directory as your flash file.
(thanks to aaaidan for pointing this out)