How can you determine if something is wood or veneer?

This article shows how to tell the difference.

http://www.erinspain.com/wood-furniture-real-or-fake-how-to-tell/

Good luck!

If you are painting it why does it matter? Sand it, prime it and paint it.

http://homeguides.sfgate.com/difference-between-wood-composite-veneer-laminate-100725.html

If you sand too much, and it is veneer, you will take it right off. Veneer is a thin sheet, and you can usually see the edge.

If you are painting:

1. Lightly scrub the surface with a deglosser and steel wool,
2. Wipe off residue/dirt with a dampened textured cloth or old towel.
3. Let dry thoroughly.
4. Use a high-adhesion primer.
5. Apply top coat.

Ask Google.

Check at corners or at seams where pieces meet. You may be able to see the thin layer on top if Vaneer.

doesnt matter which if you are painting white. Just paint!

I agree! It doesn't matter! Just lightly sand with 220 grit sandpaper to remove any gloss and roughen the surface for paint. Prime with a good stain blocking primer like Zinsser 123, BIN, or Kilz. Then paint. Seal with at least three coats of a water based polyurethane. Use a foam roller and foam brush for a smooth finish.

Veneer is a wood, just a very thin slice of it. If you want to paint, as others have said, just paint, the veneer doesn't matter. However mantels are not usually veneered. (to the best of my knowledge)

Veneer is a thin piece of wood glued to a solid wood base. If you can see seams in the piece it is probably veneer. You can paint veneer but just barely rough up the surface to accept the paint. Don't use a sander on it because it will damage the veneer and the paint will not be even.