Good Questions: How Do I Stain Veneer?

Rachel is asking for advice on transforming the color of a desk: "I have a great Jay Desk from West Elm, but its original oak finish (now discontinued) does not match my new furniture. I am hoping to convert it from an oak stain to a chocolate color. Any suggestions how to do this so I don't fully cover the wood grain but still achieve a uniform color?...

(Note: Include a pic of your problem and your question gets posted first.

Email questions and pics
with QUESTIONS in subject line to:
newyork(at)apartmenttherapy(dot)com)

...
Thanks,
Rachel"

Rachel's desired color:

Pin it button big

While we personally like the look of mismatched wood, we understand that many people do not. Because thin veneer leaves little room for correcting mistakes, you might consider painting the desk a color. Do any readers have experience staining a thin veneer?