Veneer dining tables are covered with a thin layer of decorative and functional material (usually wood, but laminate can be used as well). Just by looking, you won't easily tell the difference between cherry-veneer covered tables and solid cherry-wood, for example. Veneer dining tables require similar care and cleaning as wood furnishings. You can use water for cleaning veneer, but avoid leaving standing water on the surface if the veneer is wood.
Dust veneer dining tables frequently (at least once a week). Dust tends to attract more dust, and over time this will make the veneer look dull.
Use place mats and coasters when dining at the table. This will protect the surface from condensation from glasses and heat from pots or plates.
Clear and clean the table soon after dining. Spills left untended are likely to leave stains on the veneer--wipe them with a damp cloth as soon as you see them. For hard-to-remove food spills, use a soft cloth to clean the table. Use water and a mild detergent if necessary, and rinse the table well to remove traces of the detergent, or it can leave the finish looking dull.
Use a polish that the table's manufacturer recommends for the finish on your wood veneer dining table. If you dust your table frequently with a soft cloth, this should be sufficient to keep its polished look most of the time. The Oak Store in Mesa, Arizona, recommends polishing only once every six months.
Laminate veneer should not require polishing (except with a soft cloth).