how to get more veins on muscle

Primarily ,the speed of the blood flow and it pressure on the veins while training and with the  repetition for long periods  the size of the arteries and veins get stretched and it size get increased  naturally with time to simulate  the increase in muscular exertion .

As for the point of showing veins its depends on reducing the percentage of fat above the muscle, as well as extra water , 

In order to make them  appear larger  :

Increase the number of iterations over 15 and ,sets 3 ( light weight ) and  taking  small doses of creatine helps a lot in  increasing muscle mass and stiffness , 

for the diet you must get more  proteins and less starches and carbohydrates as much as possible  .