When I was living alone in my studio apartment, I admit it, I let both dogs beg at my feet or on the couch next to me as I ate (I didn’t have a table or desk where I could eat).  For me, this was not a big deal.  They had excellent leave-it cues and would never take food from my plate (even if left alone) and would keep their noses away from my plate as I ate.  They would also lay down at my feet and leave guests alone when I asked–so I never felt it was a problem, and it wasn’t.
That all changed when I moved back home.  With one dog and three cats in the house, dinner time was already pretty crazy.  Cats would be wondering around, checking out what’s for dinner, Bandit would be dutifully sitting right next to my mother waiting for dropped morsels…now add in my two dogs and it got slightly crazier.  It didn’t take both dogs long to figure out my mom is a bit of a pushover (for the dogs) and will give in to the puppy eyes.  Shortly after becoming acclimated to the new home, my mom found herself fending off three dogs during dinner.
This wasn’t terribly difficult for me, I mean, I had peaceful meals but I figured the RIGHT thing to do was to remedy the situation for my mom.  Now, while I love Bandit, he is my mother’s dog and is …. not held to very high behavioral standards.  She accepts his begging with no problem but my two pushy dogs were…less polite in their begging.
I decided to create a very regular and predictable dinner time routine to help with the dogs’ begging.  Every night as our dinner finishes cooking, the dogs–ahem my dogs–are sent to their places for the duration of our dinner.  Teaching them to go to their place was not terribly difficult but getting them to relax and not just stare/drool/whine was a little bit more difficult.
I used two behaviors that the dogs had a basic understanding of to regain control of dinner time.  Shayne is sent to her bed and Rio goes into a crate (with open doors).

Rio learned  to go in his crate through “Crate Games” (excellent DVD).  He hadn’t gone too far in the program so we definitely had to work on the concept of STAYING in the crate with the doors open with high distractions.  I wanted him to actively be making the choice to stay in the crate.  I did some work during non-dinner hours to help proof him on staying in the crate.  Now during dinner I would send him to his crate and in the beginning I would shut the door for part of diner and open it for part of dinner.  This was done mainly as a way to help him learn to settle–I initially tried with the door open since he rarely left the crate, but he would stare and inch his way toward the door.  Once he got the routine of going in the crate and immediately settling with the door closed, it was left open the whole time (unless he tried to exit the crate, then it was shut).  It probably took two weeks of the same routine for me to easily be able to send him to his crate and for him to be settled for the entire meal time–regardless of the movements the people would make.

Since Shayne had a reliable “go to bed” cue, I started with that.  Like with Rio, Shayne’s “go to bed” cue meant “go get on the bed” but there was no requirement of relaxing.  So for Shayne, I did some extra work during the day on adding relaxation (or a relaxed “down” position) as a piece criteria to earn a reward for that cue.  She would occasionally leave her bed and I would simply send her back to her bed (leaving the bed was never reinforced with any type of reward).  Over time, Shayne got the picture that during dinner she wasn’t going to get hand outs and started to relax and even sleep while on her bed.
Not too long ago we had a Steeler Party at our house.  We had 6 friends come over to watch the game.  Now, we have snacks out all game, but during halftime we normally get the main courses.  The dogs were hanging out and being slightly beggy during the first half (a completely tolerable level of beggy) but when it was halftime I sent them both to their places.  One of our visitors commented, “Wow!  That is amazing!  They just go there and stay while you eat? Wow!”  Even with 8 people walking around, both dogs remained on their spots until I released them.  It was great to eat without the dogs–ahem, my dogs–begging or bothering all of our guests.
It took a little time but it was not terribly difficult to teach two dogs with a long-standing history of begging to stop begging and give people space to eat.  I didn’t need to yell or “claim the space” … simply reward them for making the right choices (though the regular food rewards faded quickly and they got a jackpot at the end of dinner for waiting).