Begging and Scavenging
The easiest way to deal with begging is not to let it start in the first place. Never feed your Lab from the table or offer him scraps while you're cooking. It's a sure route to a Lab that will be constantly underfoot, hoping for a tidbit. That's not only annoying, it's dangerous. You could trip over the dog while you're moving around in the kitchen, injuring one or both of you.
Feed your Lab his meal before the family eats. His hunger will be assuaged, and he'll be less likely to bother you at the dinner table. If he's allowed in the room while the family is eating, put him in a down/stay. Do the same thing if he likes to hang out in the kitchen while you're cooking. Choose a corner away from where you're working, and require him to stay there.
Besides begging for food at the dinner table, all dogs love to raid the trash. Often, the best way to deal with your scavenging Lab is deterrence. Place contact paper (sticky side up) over the top of the trash, keep the trash behind closed doors (store it beneath the kitchen sink and put child locks on the cabinet doors) or use a can with a tightly fitting lid that your Lab can't remove. Problem solved.
If you can't resist giving your dog a treat while you're preparing a meal, make him sit or do a down first. Then send him back to his place. Only give him treats when you've called him to come and then required a sit or down.
If that doesn't work for you, make getting into the trash counterproductive. If your Lab enjoys playing with empty paper towel rolls — which can make great dog toys — and pulls one out of the trash, take it away. Later, you can give him a different roll to play with. Eventually he'll learn that paper towel rolls that come from you are fair game; those raided from the trash get taken away.
Catch your Lab with his head in the trash? Lob a shake can at the side of the trash can. The noise will startle your dog into pulling his head out. This works best with metal trash cans; plastic ones won't produce as much noise. Still, the thud should startle your dog. Then you can praise him for not being in the trash — “Good no trash” — and put the can away.