Donna: Chalk paint is super easy -- with no special preparation!
Sand the tabletop by hand using a fine-grit sanding sponge or sandpaper and a sanding block, working in the same direction that the wood grain runs. Sand through the finish just enough to reveal the bare veneer. Remove the finish around the tabletop edge using a fine-grit sanding sponge.
I agree chalk paint is the easiest especially if the veneer is in good shape! Also Gel stain works great over veneer! No sanding required!
Here is a table I recently did in gel stain. Here is a tutorial for using gel stain!
Hi Donna, if the veneer isn't missing any pieces and is in good shape you could lightly hand sand it and then paint it. If the veneer is missing pieces you can fill in the gaps with wood putty and then sand it smooth to produce a flat final product.