What do you put down for hot casserole dishes on your dining room
Table so you do not burn the tablecloth. Some kind of mat or stand??
Suggestions?

Most any type of trivet will do. Visit Amazon and search for "trivet" to get an idea of the possibilities.

Fat marble/ceramic/clay tiles are good too. A cutting board in a pinch, or a lazy susan.
A real trivet has tiny feet to keep the heat from going through to a delicate table or cloth.

Thanks a million

Hey make 'hot pads' for things like that. Wal Mart or any department store carries them. They are usually in with the table cloths and other kitchen décor.