Examine a wood table for veneer damage. Look for any outward signs of flaking, peeling or blistering. The main damage would be the entire length of the table, but a few sections at the edges can be restored with specialty glue.
Use trisodium phosphate solution to remove old veneer and glue in large sections. For small sections, take off the old glue by using a sharp tool, like a screwdriver with a flat edge. Old glue will appear bubbled at the surface, or a flaky whitish color.
Dip the end of the screwdriver in hot water. Don't use chemicals for small sections. Take the screwdriver and gently scrape at the surface of small sections until the bubbling or flaking is removed.
Glue the veneer to the core of the wood if it is salvageable. Apply pressure to the newly glued sections by using clamps, or weights. Make sure to remove any excess glue before placing weight or clamps in place. To protect the wood from pitting if using clamps, place a thin, cloth rag over the surface of the table, once the excess glue is removed, to keep the clamp from making and indentation mark on the wood.
After the glue is completely dry, delicately sand the repaired area with a chisel. If the whole table top has been glued, use 150 grit sandpaper. Apply a new veneer finish with a clean paint brush over the sanded area. Try to restore piece to its original state by using similar color veneer, or clear veneer. Let the first coat dry. Sand the first coat very lightly with low grit sandpaper once dry, enough to rough the surface a little, but not remove. Apply a second coat of veneer. The second coat will absorb into the underlying coat, and leave a slick finish. Let the second coat dry completely before placing any type of decorative items or tablecloth on top.