I have small teeth and a slightly gummy smile. I want big white teeth. How would I get a look like this using veneers? (Photo)

It is possible to do Gingivectomy and/ or crown lengthening and additive veneers to create that look.   10-12 teeth for a full smile.I would rather see you grow your maxilla orthopedically with the DNA Appliance first ant then finish with Veneers for the best long term results.   Both methods can give you a full wide smile

I just did a case just like yours on a friend. Couple of things to keep in mind one you can do a new smile preview of what you would look like after everything called a new smile preview that ive attached. But youre not only going to need gum surgery but a different type of surgery called crown lengthing (literally meaning to lengthen the crown of your teeth to make them longer). Then have the veneers placed. 
I would wait about 4-6 weeks after the surgery to have the veneers finally placed because your gums will heal and could need a slight touch up. 
Hopefully this helps 

Hi:You would need full clinical exam and xrays to get precise advice, however, one choice could be either gingivectomy or crown lengthening to remove part of the gum and place porcelain veneers to create longer bigger teeth.

You can only make the teeth as long as your bite allows, which wouldn't be much longer than what you have now. But you might be a candidate for gingivectomy, removing some of the gum tissue to expose more tooth. Once that's healed, you can explore the option of veneers if you're still unhappy with the length, shape, and shade. 

Based on the photos, you appear to be a good candidate for gingivectomy (remove excess gum tissue), and porcelain veneers to improve color, shape and harmony of your teeth. Seek an experienced cosmetic dentist who has great photos and reviews.