How to remove a spot on a veneer?

Please post a close up photo so that we could take a look.  The veneer may need to be replaced to get the root of the problem.  No pun intended. 

Discoloration of veneers is likely not repairable. Consult with your cosmetic dentist.Best of luck. James Asaf, DDS

Photo? Spots on the veneer itself can indicate porosity, crack, or stain. Veneers are usually ceramic, but can also be composite. If ceramic, very little chance of repairing predictably in the mouth, it must be cutoff and redone. The tooth can have decay, or die (necrotic), causing darkness. Smoking, coffee/tea, are notorious for staining.  Needs to be evaluated by a licensed dental professional for your options of care.Be sure to consult a local dentist before proceeding with any treatment related to your dental health. Hope that helps!

without seeing yr photo , its difficult to say anything. so, please upload photo, so we can guide u in proper way.

I would suggest you set up a consultation with your dentist to review your options.  The fix may be as simple as polishing/ drilling out the spot and bonding with a small resin filling or you might need to have the veneer replaced.