Become a blood donor . Just kidding. I have heard, though, that there is a patch you can put on that numbs the site, so it doesn't hurt as much to get the injection. That's about the best I've heard. Commonly people will say not to look when they put it in, take a deep breath, etc...I'm sure all those are helpful too. I don't know that that will help the fear, but it might lessen the pain.
For children, requesting a pediatric nurse to give the shot, or insert the IV can help a lot. Pediatric nurses are trained to deal with little ones and to help them to deal with their fears. There are also topical medications that can be used to make the needle insertion less painful. Distracting techniques can be very helpful for these patients, and the pediatric nurse is the one trained to use these techniques.
For adults, it's a more difficult situation because the fear is more deep-rooted. Again, there are topical medications that can be used to lessen the discomfort, and self-developed distraction techniques can help a lot, as well. Find out what works for you. Some prefer to look, others prefer to look away. For some patients, if the person using the needle will start by engaging the person in conversation about something of interest to the patient, it can be helpful. It's a matter of trial and error, I think, to see what works for a particular individual.