Neurogenesis is just a fancy word for nerve cells in the brain being restored. When your cells are still young and strong they are constantly being repaired and re-generated from factors that you really don't have control over. Exercise and a good diet can definitely promote a healthy environment for this to take place. I know that b12 and fish oils are neuro-protective. Look into nootropics. Some people say that Cannabis will generate neurons but I'm not sure if this is true or just more liberal biased horseshit. I'll have to look into it.
It's not really about what facilitates neurogenesis but what impedes it. Sleep deprivation, drugs-especially amphetamines, general old age, malnourishment, etc.