Is it a veneer or is it painted?

I really don't know. My guess is veneer because I can pick pieces of it off. Whatever it is, its very black and shiny. I don't see any wood grain. How could I find out?

Jane

Just the way it's flaking makes me think it's paint. Veneer loosens and bubbles and chips, but it doesn't flake like that (with little bits still sticking in a big bare area like you have, or little flakes coming off intact areas). It tends to get chipped and pulled off on edges, drawers, and comes off in 1 piece (even if it's a small chip)with a very definite height difference (since they don't make it actually paper-thin), not little places all over. If the table was always meant to be painted, it could be pretty nondescript wood, no definite grain. Veneer is usually wood-grained, they make it to save money and just put a thin layer of pretty (expensive) wood (often in a pattern) glued to a basic wood. With the damage that extensive, in the middle of the table, you would have to strip everything off and repaint/reveneer (can't patch veneer that bad, in the middle of a piece, if it is veneer, though sometimes they can reveneer chipped edges and blend them in). So try a paint stripper. Then sand, tack, and repaint.

Actually, it's probably a colored lacquer, not what you'd think of as paint (though spray paints are lacquers). I don't think you'd want to spray it again through, so painting and then putting a gloss finish on top would be easier. If it's a fairly small table and you have a steady hand (and mask off the areas you don't want to lacquer), well-ventilated place to work, you can use either a spray lacquer/paint, or brush on a gloss paint and spray or brush on lacquer after the paint is dry. It'll take several thin coats of lacquer to get a deep gloss. You may want to try shellac instead - Bobsmyuncle recommended Zinnser Sealcoat (sold as a sanding sealer) as a good out-of-the-can, readily available product. I haven't used it yet.