How Do I Keep my Dental Veneers White?

Quality porcelain veneers are highly resistant to staining!  
You shouldn't have to give up coffee and red wine to maintain the white color of your veneers. Much like a quality china tea cup that comes out clean from the dishwasher, most stains should wash right off good porcelain veneers.  That being said, I would still recommend brushing with an electric tooth brush and a non-abrasive toothpaste. People who quickly build up gingival plaque should see their hygienist for a professional teeth cleaning every 3-4 months.
 

Perfectly finished veneers will have their final coat of gloss glaze still intact. This will prevent them rubbing/scratching/wearing the teeth opposite them and also prevent them from staining themselves. 
As long as this final glaze was left in tact or, if it had to be adjusted, was replaced chair side to some extent by the dentist, all you need to do is regularly floss and brush them with a medium toothbrush and book in to your hygienist visits at least every 6 months. 
Good hygienists will appreciate that veneers do not need pumice to clean them up the same way as teeth do, and will remove the tartar before the buildup is excessive, allowing for more pleasant visits and less likely damage to the veneers. 
I wish you many happy years with your new smile -

Kind regards
Thomas Dey, BDS, MSc