Add a Listener to the actor like so. Note you need an InputMultiplexer so your Stage and Screen can both handle touches. Add the Stage first so it gets clicks first, then in the Listener call event.handle() and return true otherwise the touch will bubble through and be picked up by your Screen too.
actor.addListener(new ClickListener(){
@Override
public boolean touchDown(InputEvent event, float x, float y, int pointer, int button) {
doSomething(x,y,pointer);
event.handle();//the Stage will stop trying to handle this event
return true; //the inputmultiplexer will stop trying to handle this touch
}
});
Some actors will require
Actor.setTouchable(Touchable.enabled);