Our lab used to love to dig in our trash. I asked the obedience instructor for advice, followed it and it did work. We put a mouse trap (upside down...the object is to scare, not hurt the dog) in the trash with a piece of newspaper over it. When the dog's nose bumps it, it "jumps" up in the trash. You can actually buy modified mouse traps at pet stores made for this purpose. On those, the metal trap part is replaced by something resembling a fly swatter so you get the movement and noise with less risk of accidentally injuring your pet. The traps also taught her to stay off the furniture.

Another way is to rig some empty soda cans with a handful of pennies (tape hole shut so coins don't fall out) so that when your dog tips in trash can, a bunch of cans fall down on him. The cans can also be launched towards the dog (object again is not to hit the dog but to create a loud, startling noice near it) when it is jumping, begging, or doing other undesirable stuff. You should try to launch the can without the dog seeing that it is you doing it according to our instructor.

Of course, if your dog isn't nervous about noise, neither of these will probably help. Good luck!