Study the surface of the table. Veneer comprises of timber which is sliced 2 to 3mm wide. This is glued to panels to make wooden furniture and accessories. If the table appears to have a panel pasted onto its surface, it is probably veneer and not solid oak.
Study the grain, because oak has a distinct grain pattern. Carry a photo of a typical solid oak pattern when shopping for tables, downloaded from furniture and specialty sites on the Internet if you don't have an oak piece at home for comparison. If the grains in the photo match the grains on the table in question, there is a strong chance that the table is solid oak.
Study the functionality and design. Veneer is mainly used for items which have a low-key style, while oak is preferred for high-end furniture and furniture which has to appear impressive and stylish. If the table in question is built for durability more than design, such as a children's writing desk, it may be made of veneer.
Check the bottom of the table. A table that is not solid oak may be two different colors from the top and the bottom.