When doing fillers, how does a doctor know how not to hit a nerve or blood vessel?

It is extremely important for your injector to have a thorough understanding of facial anatomy.  Proper injection technique is also very important.  Choose your injector wisely.  In my office, all filler injections are performed by myself and not a nurse injector.  

Hi kimali, the best answer is through experience and training. Having a thorough understanding of facial anatomy as well as experience injecting are the foundation for avoiding complications. That being said, even the most experienced injectors can occasionally have minor complications such as bruising. 

  Hi, I have performed facial shaping and contouring procedures using dermal fillers or facial (cheek, chin) implants for 30 years.  A thorough understanding of the anatomy is required and hence the reason for selecting an experienced dermal filler injector.  This must then, in addition, be combined with knowledge of the proper aesthetics of facial beauty (as outlined in my book on face and body beauty) so the filler is placed "just right" in order to create a naturally, more attractive face.  Hope this helps.