Any parent can tell you that manners don’t come naturally and that it’s not the easiest thing to teach.  But it can be done.  Here are some hints.

Start early. Even toddlers can begin to pick up the basics. Teach them to say "please" and "thank you," for example.  By age 4 or 5, most kids are ready to learn more. Sure, preschoolers can be wriggly and impatient. But, most children this age can grasp what's good mealtime behavior.
Explain why manners matter. Talk to your youngsters about why being polite is important. Point out that others enjoy well-behaved company when eating a meal.

Focus on progress, not perfection. As much as you are able, keep discipline at the table to the minimum. Try not to harp on lapses in good manners. Give firm, but gentle, reminders instead.
Give rave reviews. Dish out plenty of praise for good behavior at the table. Be as specific as you can. For example: "You did so well asking nicely for another glass of milk."

What else can help?  Take a look at other ideas here.