It is very possible to teach your dog to help you clean up. In fact, it might even be easier than you think. You just might realize just how much your dog loves to help out too.
While teaching this trick, if your buddy starts to pick up trash when you have not told him to, simply ignore him and don't reward him for doing it unless you've asked. It's fairly normal for your dog to pick up items on his own while he is learning to do this trick. After all, he is probably hoping to exchange the trash for treats, but he will need to learn through practice that he only gets treats when you tell him to pick something up.