Give your dog plenty of exercise to prevent begging out of boredom or excess energy.
Exercise
Feed your dog enough on a consistent schedule so they don't beg due to hunger.
Feed
Crate train your dog to give them a place to relax while you eat without begging.
Crate
Reward good behavior with treats when they are calmly settling nearby as you eat.
Reward
Firmly correct begging, rewarding silence. Be very consistent.
Correct
Completely ignore all begging behavior, no eye contact or verbal cues.
Ignore
Separate dogs/puppies during meal times until begging is fully trained out.
Separate