This was the phrase I often used and I think helped set the tone for the (mostly) lovely manners we still enjoy years later.
"Would you like some more carrots, or no thank you?"
"Would you like a cracker, or no thank you?"
The almost-toddlers and toddlers may not be able to serve themselves, but when you hold out that cracker or offer carrots you can model the language. With lots of little ones doing sign language, they can often sign for "more" or "all done" pretty early. This was handy for us, and M was adept at the "more" sign pretty early...
When you pass a plate or something to your partner or others at the table, say "please and thank you." Hubby also made a point to thank me for making such a nice dinner, and I thank him when he cooked. It does help to make the table a more pleasant and centered place, which can be tough when little ones are at the table with all the joy, mess and energy they bring!