Two of my dogs actually seem to not care much [when we eat], the other two are quite interested in our dining experiences. So how does one do it?
First, if you ever feed your dog while you are eating or sitting down in the location where you normally eat your meals, then this may take extra care and dedication. I don't recommend you feed your dog "from the table". Feed your dogs when you feed them their meals and when you are training, that's it. It's more of a respect thing than anything else. You also can't realistically expect your dog to stay away from your meal if you've been feeding him some pieces every now and again.
If your dog only eats when you feed him/her then this will be much easier for you. I suggest teaching your dog to "Leave it", and enforce that they know this means "leave it alone permanently!". If you find yourself saying "Leave it" over and over again then they may need a little brushing up on this command!
Give a "Leave it" and then ask your dog to go lie down away from you at least 3 feet or more. If your dog can lie at your feet and not beg, and you don't mind this, then you can do that too.
It's best to teach your dog that "sit" and "down" mean that they each have an implied "stay" along with that. So, if you say "Fluffy, sit" then she should do that until you tell her otherwise. Remember to use a release command and always release your dog from every command once you are finished. For example, when you ask your dog to sit at any point, e.g, before you toss a ball for her to catch, then say "okay!" to release her from the sit and she can be allowed to go get the ball. Always release your dog. They will soon learn that they cannot do anything until they hear the "okay" [release command].
Another great thing to add in is a specific spot or location for the dog to go to while you are eating, or for any other time. At my house I use this to keep the dogs out from under the highchair since my 16-month-old feeds the dogs from there and they are easier to train that she is!
You can use a rug, mat or bed or even just an area. My area is the carpet in the bedroom that divides the kitchen and the bedroom. This way they are out of the kitchen and away from the highchair altogether. Teach your dog a command for this, e.g., "get on your bed", and have him go there while you eat and stay until you tell him he is released.
Here is a video of a puppy I was babysitting at my house and I taught her to do this with a bath mat. The video doesn't show me teaching her but the results. So, how did I do it? Watch the video and then see the how-to below.
1) Get a bunch of yummy treats.
2) Lure the dog to the mat with a treat. You can do this by having them literally follow you to the mat because they follow the hand with the treat or by tossing the treat onto the mat.
3) The critical point is this: the very second a paw touches the mat you praise and treat --"Good girl!" [give treat].
5) Start to phase out luring to the mat and only stand next to the mat and wait for the dog to go to it. Praise with good timing.
6) When the dog begins to go to the mat in anticipation of a reward then add in your phrase command. Here it was "Get on your mat."
7) Slowly get further and further from the mat.
The key is timing. You have to reward just right and right on time. Don't add the phrase in too soon and don't stop luring or get to far from the mat too soon. It may take longer for each dog.