How do you style your dining table or kitchen table when not in use?

I don’t think the table is too big. Personally I might think about getting a rug under the table with a stronger colour to tie in better with the sofa.

You don't say what the table is made from, can you post a picture? Depending on the value of the table, it may be cheaper / easier to buy a new extending table than to pay a carpenter to make an extension and supports for the existing one. If you are going to cover it with a table cloth and don't mind therefore, what it's made from, then MDF offers the cheapest and easiest way to make an extension, but you still need supports of some kind to keep it up, that may not be possible with the table you've got.

Wood would definitely be a feature, if you go for a natural wood as suggested above it will create a niche and be a focus point. Unless you are looking for a monochromatic design, then a white table would be the best options and you'd create the focus point with lighting or other decorations.