How do I cover or paint a white veneer/laminate piece of furniture?

Lightly sand to remove any gloss. Prime with a stain blocking primer like Zinsser 123. Then paint with your color. Seal with at least three coats with a water based polyurethane. Use a small foam roller and foam brush for a smooth finish.

I really like these chairs too. I have been chalk painting furniture lately and its great but for these you might want to clean them, sand lightly to remove any shine or gloss and restain them then let completely( over night) then put a coat of polyacrylic the wood(polyacrylic doesn't yellow like polyurethane does.).

Great save!

If you want color; clean and let dry, then chalk paint. This will take 3or 4 coats( making sure to let dry overnight between coats. Then use clear wax or brown antiquing wax, let dry throughly and buff.