Cats are known for their cleverness. It won't take a long time for the average cat to figure out that the contents of your plate are quite a bit more appetizing than what is in his dish. Once they understand that, many cats become determined to convince you to share. Purring, yowling, kneading and meowing pitifully become standard dinner accompaniments. Once the "sad, starving kitten" routine doesn't work anymore, most cats will up their game, jumping up on the table to join you or waiting until your back is turned to steal right off your plate. It's annoying and unsanitary as well as unhealthy for both you and your cat.
Purchase an automatic cat feeder. This will help the cat stop viewing you as the sole source of food--though it could potentially lead to overeating. If your cat is already overweight, this may not be a viable option.
Feed the cat immediately before you sit down to dinner. If the automatic feeder is out of the question, you will need to find some way to distract your cat while you eat. Odds are good that once the cat is no longer hungry, it will take a nap, buying you enough time to finish your meal in peace.
Be consistent. Never feed the cat from your plate and never offer the cat scraps while you are eating. It will be difficult, but try to completely ignore the cat's begging. Pretend you don't see or hear him. Bad attention is still attention and can reinforce the begging behavior. If the begging never works, they will eventually give it up.
Act like a momma cat, if you must. If the cat is very persistent and nothing seems to be changing the begging behavior, wait until the begging begins and take the cat by the nape of the neck. Give her a gentle shake and say, "NO!" and release her. This method is most effective with kittens or juvenile cats, but can still work with older felines.
Tap the cat's nose if she resumes begging when you release him. Do not hit the cat, just put your finger on his nose and firmly say, "No," again.
Reward the cat for good behavior when it finally happens. With consistency and patience, the cat will eventually give up the begging, and when he does, be sure you give her lots of petting and praise to reinforce the good manners.