When referring to organizing a dining table, I assume that you mean de-cluttering it. In most homes, the dining room table is a central area where everyone in the house puts things instead of putting them where they belong. Am I right? I have had that problem as well.
In an organized home, the dining room table is usually decorated, maybe with a centerpiece and place mats. Such decorations discourage people from cluttering it up, but it may take some training and commitment from your family.
Perhaps the best way to permanently de-clutter your dining room table is start by de-cluttering and organizing the rest of your home. If everything has a place, it is easier to get dedication from the whole family to put things away where they belong rather than piling stuff up on the dining room table.
If you haven't already, I advise you to read about Decluttering Forever. You will find some awesome tips in that article.